Youtube News: Youtube daily report w Jun 20 2017

Avoid Angela...

And I'm done!

How could Tom stand me up like this?

It's like my heart is on an elevator that's going down and Tom pressed all the buttons!

Hi Angela...

For more infomation >> THIS THURSDAY - Talking Tom and Friends | Season 2 Episode 2 (Sneak Peek) - Duration: 0:31.

-------------------------------------------

Mercedes-Benz C-Klasse C 350 e Limousine Lease Edition 7% Bijtelling, Panoramadak - Duration: 1:01.

For more infomation >> Mercedes-Benz C-Klasse C 350 e Limousine Lease Edition 7% Bijtelling, Panoramadak - Duration: 1:01.

-------------------------------------------

VIOLÊNCIA | DENÚNCIA | E você? - Duration: 5:00.

For more infomation >> VIOLÊNCIA | DENÚNCIA | E você? - Duration: 5:00.

-------------------------------------------

Evolua e não se deixe afetar por objetivos do passado - use sua razão e progrida. - Duration: 1:59.

For more infomation >> Evolua e não se deixe afetar por objetivos do passado - use sua razão e progrida. - Duration: 1:59.

-------------------------------------------

Citroën C1 1.0 E-VTI 68 5-DRS Selection - Duration: 0:56.

For more infomation >> Citroën C1 1.0 E-VTI 68 5-DRS Selection - Duration: 0:56.

-------------------------------------------

Mercedes-Benz E-Klasse Coupé 200 CGI Avantgarde - Duration: 0:58.

For more infomation >> Mercedes-Benz E-Klasse Coupé 200 CGI Avantgarde - Duration: 0:58.

-------------------------------------------

2 Dicas para Fazer o seu Negócio dar Certo! - Duration: 4:42.

For more infomation >> 2 Dicas para Fazer o seu Negócio dar Certo! - Duration: 4:42.

-------------------------------------------

DIY Dicas de decoração para Festa Junina - #festajuninadiy - Artesanato do Compartilhando Arte - Duration: 7:58.

For more infomation >> DIY Dicas de decoração para Festa Junina - #festajuninadiy - Artesanato do Compartilhando Arte - Duration: 7:58.

-------------------------------------------

Mayview firefighter dies, another injured in the line of duty - Duration: 1:24.

A MAYVIEW FIRE

FIGHTER HAS DIED IN

THE LINE OF DUTY.

ANOTHER

FIREFIGHTER IS

HOPSPITALIZED WITH

CRITICAL INJURIES

FOLLOWING A SERIOUS

CRASH MONDAY

AFTERNOON.

BOTH WERE WORKING

A FIRE SCENE ON

HIGHWAY E -- ABOUT 45

MINUTES EAST OF

KANSAS CITY.

THEY WERE BOTH HIT

AND DRAGGED -- WHEN

A DRIVER HIT 2 CARS

ON THE SIDE OF THE

ROAD.

41 ACTION NEWS

REPORTER BELINDA

POST JOINS US LIVE

OUTSIDE RESEARCH

MEDICAL CENTER WITH

THE LATEST ON FIRST

RESPONDER WHO IS

CURRENTLY FIGHTING

FOR HIS LIFE.

33-YEAR-OLD JACOB

HAYWARD IS

CURRENTLY IN

CRITICAL CONDITION.

PARAMEDICS LIFE-

FLIGHTED HIM HERE...

AFTER A SERIOUS

ACCIDENT MONDAY

AFTERNOON.

AN ACCIDENT THAT

KILLED 55-YEAR-OLD

FIRE FIGHTER JEFFREY

SANDERS.

HERE IS WHAT WE

KNOW ABOUT THE

ACCIDENT.

BOTH SANDERS AND

HAYWARD WERE

RESPONDING TO A

FIRE.

THEIR TRUCK AND

ANOTHER VEHICLE

WERE PULLED OFF TO

THE SIDE OF HIGHWAY

A DRIVER HIT BOTH OF

THEM... PUSHING THE

TRUCK AND VEHICLE

DOWN AN EMBANKENT.

SANDERS AND

HAYWARD GOT

CAUGHT UNDERNEATH

THEM.

55-YEAR-OLD SANDERS

WAS PRONOUNCED

DEAD AT THE SCENE.

FIRE DEPARTMENTS,

LIKE JOHNSON

COUNTY, ARE POSTING

TO THEIR SOCIAL

MEDIA FEEDS...

ASKING FOR PRAYERS

FOR SANDERS AND

HAYWARD.

BOTH OF THE FIRE

FIGHTERS LIVE IN

MAYVIEW.

AGAIN, AT OUR LAST

CHECK, HAYWARD IS

STILL HOSPITALIZED

HERE AT RESEARCH

MEDICAL IN CRITICAL

CONDITION.

WE WILL CONTINUE TO

TRACK HIS CONDITION

AND BRING YOU

UPDATES AS THEY

BECOME AVAILABLE.

BELINDA POST, 41

ACTION NEWS TODAY

ON 38 THE SPOT.

For more infomation >> Mayview firefighter dies, another injured in the line of duty - Duration: 1:24.

-------------------------------------------

Banindo Hackers #1 - Continuação xD - Duration: 2:52.

For more infomation >> Banindo Hackers #1 - Continuação xD - Duration: 2:52.

-------------------------------------------

Natiruts "Reggae Power" Acustico - Cover no violão - Duration: 2:09.

When night falls and the sound Bring you some good dream.

And make everything transcend Sadness will disappear and no one will suffer

Tune in to your vibration No time to live in vain

And do not think about giving up anymore There is a world that just wants to see you smile

Don't Cry Our life is even made for learning

And now It's time to try to break free, it will not hurt

Let the energy of sound take you Positive vibe released by air

Who feels with the soul is capable of loving Are you always free to sing

Ooh Natiruts Reggae Power came back Ooh Turning every night into love

Of peace and love I want much more I have not got life, I'm running after

The light of your smile at night is too much Brazil, Jaú, harmony of peace

Tune in to your vibration No time to live in vain

And do not think about giving up anymore There is a world that just wants to see you smile

Don't Cry Our life is even made for learning

And now It's time to try to break free, it will not hurt

Let the energy of sound take you Positive vibe released by air

Who feels with the soul is capable of loving Are you always free to sing

Ooh Natiruts Reggae Power came back Ooh Turning every night into love

For more infomation >> Natiruts "Reggae Power" Acustico - Cover no violão - Duration: 2:09.

-------------------------------------------

Dez razões para estudar no IFMS - Duration: 2:48.

For more infomation >> Dez razões para estudar no IFMS - Duration: 2:48.

-------------------------------------------

Lectura del Quijote (2016-2017). - Duration: 5:15.

For more infomation >> Lectura del Quijote (2016-2017). - Duration: 5:15.

-------------------------------------------

Superior vena cava syndrome - causes, symptoms, diagnosis, treatment, pathology - Duration: 6:43.

Superior vena cava syndrome occurs when blood flow through the superior vena cava is obstructed

either from within due to a blood clot or from external compression.

The superior vena cava is a short and wide vein on the right side of the chest that drains

blood from the head, upper body and both arms, and delivers all of that blood to the right

atrium of the heart.

The superior vena cava can get obstructed a few different ways, and the most common

way is via a nearby tumor, through mass effect, where inflammation and swelling pushes up

against the superior vena cava.

Alternatively, though, there can be direct tumor invasion into the superior vena cava

which is when tumor cells penetrate and grow directly into the superior vena cava.

But this is only possible if the tumor is located on the right side near the superior

vena cava.

The most common type of cancer that does this is a lung cancer, and when it's located

in the apex of the right lung near the superior vena cava, it's given the name Pancoast

tumor - after Dr. Henry Pancoast who first described them.

Also in that area, though, you've got a bunch of lymph nodes, and another possible

cause of SVC syndrome a tumor of the lymph nodes, which would could lead to compression

of the SVC.

This could be lymphomas – or primary cancers of the lymph node - cause superior vena cava

syndrome, or secondary and have spread from somewhere else, like the lungs.

Apart from tumors, the superior vena cava can also get obstructed if a blood clot or

thrombosis forms within it.

This most often develops in individuals who have a long-term device like an indwelling

central venous catheter.

Regardless of the cause, when the superior vena cava gets obstructed, behind the obstruction

you'll get an increase in venous pressure.

When this happens, blood starts to get re-routed through different blood vessels, essentially

draining into the inferior vena cava, which also drains into the right atrium.

These are now called collateral blood vessels, and are essentially alternate routes.

If the blockage is low enough, it could be through the azygos system, but also other

options are the internal mammary, lateral thoracic, and esophageal venous systems.

Over the course of a few weeks, these collateral veins dilate, after which point the venous

pressure decreases a bit, but still remains higher than normal, even after the collaterals

have dilated fully.

Symptoms of superior vena cava syndrome relate to the blockage in venous blood blow.

A decrease in venous return of blood to the heart, means that less blood is getting pumped

to the lungs, leaving individuals feeling short of breath.

Meanwhile, the backup of venous blood and venous stasis gives individuals a flushed

appearance and swollen neck and chest veins.

It also causes edema, where fluid leaks out of the blood vessels and into surrounding

tissues, resulting in swelling of the face, neck and arms.

Sometimes the fluid build-up can cause compression of the trachea and other structures in the

upper airway.

This can cause shortness of breath as well as stridor, which is a harsh high pitched

noise heard during inhalation.

Excess fluid can also compress the muscles of the voice box or larynx, causing a hoarse

voice.

Fluid around the esophagus, can cause dysphagia which is difficulty swallowing.

Most serious of all, though is cerebral edema, or excess fluid building up in the brain,

which can cause symptoms like headaches and confusion.

Worse yet, if the cerebral edema is severe, the fluid in the tissues can compress the

tiny blood vessels supplying the brain with blood, leading to cerebral ischemia.

If superior vena cava syndrome is suspected, diagnosis can be done by chest X-ray or CT

scan can be helpful to look for tumors and visualize collateral vessels.

To look for obstruction within the superior vena cava, a radio-opaque dye can be injected

into it, while a series of X-rays are taken to visualize how blood flows through it.

For treatment, one general key intervention is making sure that a person's head is kept

above the level of the heart, because gravity can help drain fluid from the head and neck

back towards the heart.

Other treatments are dependent on the underlying cause - for example, a tumor is typically

evaluated with a biopsy to determine it's type and the how far it may have spread, and

it may be treated with radiation and chemotherapy.

In addition, sometimes steroids can be used to reduce swelling around the tumor.

If the cause is a blood clot within the superior vena cava, anticoagulants can be used to prevent

it from getting larger.

Alright, as a quick recap - superior vena cava syndrome happens when blood flow in the

superior vena cava is obstructed, most commonly from a tumor causing external compression,

but it can also be from thrombosis.

The obstruction increases venous pressure and edema which can lead to a range of symptoms

such as, stridor, voice changes, dysphagia, and even cerebral ischemia

Thanks for watching, you can help support us by donating on patreon, or subscribing

to our channel, or telling your friends about us on social media.

For more infomation >> Superior vena cava syndrome - causes, symptoms, diagnosis, treatment, pathology - Duration: 6:43.

-------------------------------------------

Hubert Kempf, Alghero 16 giugno 2017 - Duration: 5:21.

For more infomation >> Hubert Kempf, Alghero 16 giugno 2017 - Duration: 5:21.

-------------------------------------------

LikeLikeNatsuMeloポポリコ替え歌：独り身芳恵(元歌：ひとり三好へ：角川博) - Duration: 4:02.

For more infomation >> LikeLikeNatsuMeloポポリコ替え歌：独り身芳恵(元歌：ひとり三好へ：角川博) - Duration: 4:02.

-------------------------------------------

Curso completo sobre cómo reducir niebla al pintar con airless (1/8) - Duration: 5:09.

For more infomation >> Curso completo sobre cómo reducir niebla al pintar con airless (1/8) - Duration: 5:09.

-------------------------------------------

Cottage cheese-sour cream dessert with strawberries, delicious recipe! - Duration: 5:05.

Curd and sour dessert with strawberries, a recipe for a delicious and easy dessert!

If you get in the way of subtitles - turn them off!

Hello! My name is Dina. And I'm very glad to see you on my channel "Collection of Recipes".

Today we continue a series of delicious strawberry desserts. Prepare cream cheese and sour cream with strawberries.

Everyone knows that cottage cheese is very useful for young growing organisms, as well as for those engaged in fitness and watching their figure.

And in combination with fresh strawberries, this product is not only useful, but also very tasty!

The advantage of the curd-strawberry dessert is that it is low-calorie and very easy to prepare.

Correctly cooked curd dessert has a homogeneous, without lumps, air structure, more reminiscent of ice cream

And therefore will have to taste even to those who do not like cottage cheese.

Today I will show 2 types of cottage cheese-sour cream dessert with strawberries, for the preparation of which we will need:

• 400 gr. Cottage cheese • 400 gr. Sour cream • 500 gr. Strawberries

• 1 tbsp. Sugar • 40 gr. Gelatin (2 tablespoons)

• 100 ml. Milk • vanillin

First you need to soak gelatin.

Pour the gelatin into the milk, mix well until the lumps dissolve and set aside for swelling.

We take the cup, in which we will mix all the products.

We spread into it cottage cheese (use cottage cheese of any fat content, though skimmed),

Add sour cream (instead of sour cream you can take not fatty yogurt or milk),

Pour out sugar (or honey at will),

And vanillin.

Then, using a submersible blender, we crush the products into a homogeneous air mass without lumps.

While we set it aside and deal with strawberries.

Separately we put aside the most beautiful strawberries for decorating the dessert, they will be needed later.

And since we will serve dessert in two different ways, then strawberries must be prepared for each of them.

For a dessert with a white base, you need a strawberry cut into 2 halves.

We cut a piece of strawberries in half,

And the rest is left as a whole, it will be needed for a "pink" dessert.

We will serve the first dessert in flat glasses on a high leg, lay the strawberry cut down to the bottom of the glass.

Meanwhile, gelatin is well-swollen, it needs to be melt to liquid state, it can be done in a microwave or in a water bath,

The main thing is not to allow the boiling gelatin, otherwise it will lose its gelling properties.

Gelatin is melted, and whilst continuing to pour, pour it in a thin trickle into the curds and sour cream mass.

A little more stir and dispense the prepared mixture into glasses.

Send the dessert with the white base in the fridge and prepare a pink dessert.

For this, we spread the strawberries into the remaining curds and sour cream mass and punch the blender to a homogeneous state.

Pour the strawberry-curd mixture into the croissants and send the dessert to the refrigerator until it is completely solidified.

After 2 hours, the dessert can be decorated and served to the table.

Decorate it with chopped nuts, grated or melted chocolate, fresh strawberries and mint leaves, all to your taste.

Here we have such a curd-cream dessert with strawberries!

You can cook it with almost any fruit and berries, both fresh and frozen, and you need to serve it chilled.

This dessert of simple and affordable products, easy to prepare, very delicate, tastes more like ice cream and just melts in your mouth.

Prepare this dessert in advance, it perfectly keeps the shape and does not melt at room temperature.

The dessert is very beautiful, spectacular, and looks great on the festive table.

I showed the feeding option in glass crochets, although it can be prepared in silicone molds of various configurations or detachable in the form of a cake.

In the summer, when the abundance of fresh fruits and berries can be cooked various delicacies, for example, here is such a dessert

Or light fruit cakes without baking, I have a recipe for this cake on the channel, I'll leave the link in the description under the video.

Cook with pleasure! I wish everyone a pleasant appetite!

If you liked this dessert - put your finger up! Share it with your friends and leave a comment!

Subscribe to my YouTube channel - "Recipe Collection" and click on the bell to receive notifications of new videos.

I have other dessert recipes on the channel, see if you're interested.

All links on the screen and in the description.

Dean was with you.

To new meetings, to new delicious recipes!

#NoMoreCraptions

For more infomation >> Cottage cheese-sour cream dessert with strawberries, delicious recipe! - Duration: 5:05.

-------------------------------------------

Mercedes-Benz R-Klasse 280 CDI 4-MATIC - Duration: 1:02.

For more infomation >> Mercedes-Benz R-Klasse 280 CDI 4-MATIC - Duration: 1:02.

-------------------------------------------

Renault Clio 1.5 dCi Dynamique (14% BIJT.!!/Climate/Camera/R-LINK) - Duration: 1:00.

For more infomation >> Renault Clio 1.5 dCi Dynamique (14% BIJT.!!/Climate/Camera/R-LINK) - Duration: 1:00.

-------------------------------------------

ONE MORE CHALLENGE... - Duration: 10:27.

For more infomation >> ONE MORE CHALLENGE... - Duration: 10:27.

-------------------------------------------

Peugeot 207 1.6-16V T FÉLINE - Duration: 0:59.

For more infomation >> Peugeot 207 1.6-16V T FÉLINE - Duration: 0:59.

-------------------------------------------

La seule petite chose qui t'empêche d'être heureux - Duration: 3:17.

For more infomation >> La seule petite chose qui t'empêche d'être heureux - Duration: 3:17.

-------------------------------------------

Opel Mokka 1.4T 140PK INNOVATION - LEDER - NAVIGATIE - OPENDAK - RIJKLAAR - Duration: 0:59.

For more infomation >> Opel Mokka 1.4T 140PK INNOVATION - LEDER - NAVIGATIE - OPENDAK - RIJKLAAR - Duration: 0:59.

-------------------------------------------

Opel Mokka 1.4T 140PK INNOVATION - LEDER - OPENDAK - NAVIGATIE - RIJKLAAR - Duration: 0:44.

For more infomation >> Opel Mokka 1.4T 140PK INNOVATION - LEDER - OPENDAK - NAVIGATIE - RIJKLAAR - Duration: 0:44.

-------------------------------------------

Opel Mokka 1.4T 140PK INNOVATION - NAVIGATIE - LEDER - OPENDAK - RIJKLAAR - Duration: 0:47.

For more infomation >> Opel Mokka 1.4T 140PK INNOVATION - NAVIGATIE - LEDER - OPENDAK - RIJKLAAR - Duration: 0:47.

-------------------------------------------

Liouville's number, the easiest transcendental and its clones - Duration: 20:40.

Welcome to another Mathologer video.

Liouville's number the monster up there

consists of infinitely many isolated

islands of 1s at the 1! th, 2! th,

3! th, etc. digits with

exploding gaps of zeros between them. As

I promised you at the end of the last

video, today's mission is to show you a

nice visual way of seeing that this

number is transcendental. I'm pretty

convinced that as far as transcendence proofs

for specific numbers goes, what I've put

together here is as simple and as

accessible as it will ever get. Still, if

you make it to the end and understand

all my arguments I think you can be

pretty proud of yourself since not even

that many professional mathematicians

know any transcendence proofs. And, if you

make it to the end, I've got a special

treat for you. I'll show you how you can

use Liouville's number as a template to make

a clone of the real numbers within the

real numbers. This clone is made up of

transcendental numbers like this strange

cousin of Pi, but perhaps the craziest

thing about this clone is that although

it is as large at the set of real

numbers itself, it is of measure 0. This

means that in a sense it takes up no

space within the real numbers. For those

of you in the know this set is closely

related to Cantor sets.

What's a transcendental number again?

Well for a detailed introduction just

watch the last video. So here just real

quick: the transcendental numbers are

defined in terms of what they are NOT.

They are NOT among the real numbers that

you encounter when you're doing

classical algebra, like the integers, the

rational numbers, any of the real numbers

that can be written as rooty expressions

like these, or any of the real numbers

that pop up as solutions to polynomial

equations with integer coefficients like

these. This last set of numbers is called the

algebraic numbers and includes all the

other types of numbers that I mentioned

before: integers, rationals and rooty

numbers. Anyway, we call a real number

transcendental if it is not algebraic,

if it is not a solution of a

polynomial equation with integer

coefficients. Liouville's number or Liouville's

constant was shown to be transcendental

in 1851 by the great French

mathematician Joseph Liouville. It was one of

the first numbers shown to be

transcendental and Liouville's proof of this fact

is probably the easiest transcendence

proof for any specific number. Liouville's

proof is accessible to anybody who has

had some exposure to proofs at

university level real analysis and I have

concluded links to the original French

paper and a modern version of the proof

in English in the description. But since

many of you would struggle with any of

the proofs in these papers or in

textbooks, I've tried to come up with an

alternative way of seeing the

transcendence of Liouville's number that can be

understood and hopefully also enjoyed by

anybody who watches these sorts of maths

videos, including all Mathologer fans who

are still in high school. I'm still

working on the primary school version

but and I am probably never going to get there.

Okay, Liouville's number, lots and lots of

0s and 1s and the 1s are the 1! th,

2! th, 3! th, etc.

digits. Just a quick reminder, 1!

is equal to 1, 2! is 1 times 2 is

equal to 2, 3! is 1 times 2

times 3 is equal to 6, 4! is 24.

Then 120, 720, 5040, etc. a sequence of

numbers that grows rapidly which means

that the stretches of zeros between

consecutive 1s get longer and longer

extremely quickly. Okay, here then is my

proof that Liouville's number is

transcendental. Let me know in the

comments whether this proof works for

you. When dealing with a complicated

number like pi

approximate value often suffice or are at

least a good place to start. To get such

an approximation we often chop off the

decimal expansion at some point.

Now let's approximate the number pi

squared with the squares of these

truncations.

Then these approximations for pi squared

will be spot-on

to a certain digit and may be good enough

for some application we have in mind.

However from some point on these

approximations or go off target. For

example, the last approximation down

there coincides with pi squared in only

the first four digits and the remaining

digits that you can see here are wrong.

Liouville's number L behaves quite

different in this respect. But to start

with the only distinguishable

truncations are those that cut off

after the 1s and these are the first

four of these truncations of L. Now

squaring gives these numbers here and in

contrast to what we had before all the

digits of the squared truncations seem to

be correct. And looks are not deceiving,

this is actually always true and the

reason for this is not too hard to pin

down. It's because all the nonzero digits

of Liouville's

number are spaced further and further

apart and those further down the line

simply don't play any role in producing

the earlier digits of the square of our

number. For the moment I'll gloss over the

technical details but I'll return to

them after I've finished

outlining the proof. Anyway, what happens

if you raise L to a different power, say

5? Well then, as you can see, while the

approximations are still definitely damn

good, things are no longer spot on

for all digits. Here, for example, one digit

is wrong and here three but if you look

closely you'll find that the next

approximation is spot on again, all

digits are correct. And actually things

will be spot on from this truncation on.

So, all digits of truncation L_5^5, L_6^5,

and so on will be correct. In fact,

something similar will be true for all

powers. S,o as we've seen, all squared

truncations are spot on. The same turns

out to be the case for the cubed ones,

fourth powers too, fifth powers we've

already seen that all digits are spot-on

from a certain truncation on. Same thing

for sixth powers, except this happens a

little bit later, and so on, for all

powers. Now,

if instead of just power we look at any polynomial with positive

integer coefficients: all pluses no minuses up there, right? So, if instead of just powers

of the number L we're approximating a polynomial like this, evaluated at the

number L, then we find that all the digits of our approximations will be

correct from some truncation onwards. In particular, in the case of this

polynomial all digits will be correct from L_2 onward. We're getting pretty

close to the punchline. Remember what we have to demonstrate is that L does not

solve any equation like this. To get the proof going we first move all the

negative terms to the right side. Now this results in two of those special

polynomials that only have positive terms, one on the left and one on the

right side of the equals sign. Now let's assume that L actually is a solution of

this polynomial equation. This means that the number on the left of the equals sign

is actually equal to the number on the right. I'll call this number the number

at the top. Let's see what numbers we get on the left and right when we replace L

by one of its truncations. Let's start with L_1 and work our way up. Obviously

the higher the truncation the better approximations for the number at the top

will get on the left and on the right but we also know that in addition to

this all digits of these approximations will be correct from some truncation on.

For the sake of argument, let's say that this is the case from L_5 onward. What

this means is that now the first digit of the approximation on the left is equal

to the first digit of the approximation on the right, the second digit on the

left is equal to the second digit on the right, and so on, for a while, until.... Well

you'd expect one of the two sides to run out of nonzero digits and the other side

to keep on going before it stops. Alright and maybe that's exactly what will

happen. However, surprisingly, and we'll see why

when we go all technical, at this point our assumption that L

solves the equation also implies that, starting with a possibly higher

truncation, let's say L_6, we will always run out of nonzero digits at the same

time in both approximations. So this means that our two approximations are in

fact equal from this truncation onward and this means that just like L itself L_6

and all the following infinitely many truncations are also solutions to our

polynomial equation. But infinitely many different solutions are impossible

because a polynomial equation can only have as many solutions as its degree. For

example, our degree 6 polynomial can have at most 6 solutions and so the

assumption that our number L solves a polynomial equation with integer

coefficients leads to the absolutely impossible conclusion that this

polynomial has infinitely many solutions. And this means that our assumption that

L solves an equation like this was wrong in the first place and that means that L

is a transcendental number. Very neat proof by contradiction, right? Of course

what I did not show you is that all the approximations will eventually be spot on

no matter what polynomial equation we're dealing with. Okay, let's have a closer

look. The different 1s in our number L

stand for different powers of 10. For example, the first one stands for 10

to the minus 1, the second for 10 to the minus 2, the third for 10 to the minus 6,

and so on. And the number L is just the sum of these powers of 10. Now we started by

pondering L squared so let's have a look at how we would calculate this number.

Actually before we do that, let's calculate the square of the second

truncation. Okay, so here we have to multiply every term at the top with

every one at the bottom and then add up. So 10 to the minus 1 times 10 to the

minus 1 is 10 to the minus 2, 10 to the minus 1 times 10 to the minus 2 is 10 to

the minus 3. This times that that, 10 to the minus 3 again. This times

that 10 to the minus 4. Add up everything to get the square we are after. For L squared

we have to multiply again every term at the top with every one at the bottom and

then add up. Hmm, might take a while, right? So 10 ^ -1

times 10 ^ -1 is 10 ^ -2, minus 1 minus 2 minus 3,

minus 1 minus 6 minus 7, and so on. Minus 2 minus 1 minus 3, minus 2 minus 2 minus

4, and so on. And so on. Now why are the digits of the square truncation correct?

Well, its rightmost digit 1 comes from multiplying the rightmost term of the

truncation with itself. For the other terms to interfere with the digits of

the square truncation, one of the terms outside the box at the top multiplied

with one of the terms at the bottom should be at least as big as

10 ^ -4. But the largest number we can make this way is 10 ^ -6 times

10 ^ -1 which is 10 ^ -7, a lot smaller than e

10 ^ -4. Okay so there's no danger here. What about these critical numbers for

the next truncation. Also no danger and to gap between the exponents minus 12

and minus 25 is larger than before, so even less danger. One more. The gap has

increased even further. Now it's a one-liner to show that this trend

continues and I actually leave it to you to sort out the details, and, well,

actually you only get partial credit if it takes you more than one line. Let's

have a look at all this for the fourth truncation of the fifth power of L.

That's the next thing we looked at, right? As I said before, all digits are correct

for this fourth truncation. Let's double check this: yes, the green 124 is larger

than the yellow 120. Tick! Again, I leave it to you to fill in the details

to show that this will also be the case for the higher truncations. Remember that

there were problems with the lower trunations. Let's see where these show up

here. Okay the order has flipped, the 30 is now

larger than the 28 and so there will be wrong digits in the approximation. One

step down there's also trouble with the green terms interfering with the digits

of the power of the second truncation. Okay so here are the first digits of L

squared. I just like to highlight again the gap between the yellow lowest terms

of the squared truncations together with the corresponding worst-case-scenario

green terms. As we've already observed this gap is increasing. In fact, it will get

arbitrarily large. And the same is true for all the other powers once the gap

starts appearing from some truncation onward. For those of you who did those

one-line calculations earlier on will already have convinced yourself of this

fact. What about polynomials with positive integer coefficients. Well,

they're built from powers. Take, for example, L squared plus L. Highlight the

second truncation. First note that the corresponding green digits are basically

aligned. That's because the top one essentially comes about from multiplying

the bottom one by 10 ^ -1 that's a shift of one position. Anyway

this relative alignment will always be the same as we move to the right. Also, as

we move towards the right, the gap of zeros in front of the green digits gets

as large as you wish. Given this gap of zeros, it is clear that when we add up L_3

and L_3 squared none of the green digits or beyond will

add to the sum within L squared, and so the digits of the approximation will all

be correct. But what happens if the individual powers in the polynomial are

multiplied by non-trivial positive constants. For example, let's multiply the linear term

by something huge, say 10. The overall effect of this changed term are it's

nonzero islands possibly growing and the greens shifting to

the left. This may lead to the overall gaps in front of the greens shrinking or even

vanishing for really large coefficients like googleplex however since the gaps

grow unlimited in size they will eventually absorb the shrinkage and gaps

will always be present from a certain point on. And this means that no matter

what polynomial we're dealing with, all our approximations will be spot-on from

a certain truncation onward. Almost there. In the final part of the proof we assumed

that L solves a polynomial equation like the one up there. I claim that this

implies that from a certain point onward all truncations also solve this equation

which then gives the contradiction. Well, as just now, we can see that from a

certain truncation, say L_5 onward, we have the usual common gap of zeros for all

the terms in this equation. But then for the identity on the left to be true,

which is our assumption, the sum of the two approximations on the top must be

equal to the sum of the two at the bottom, which is exactly what we needed

to convince ourselves of. Anyway that's basically it. Of course I could still

fill in all the nitty-gritty calculations, for example about the ever

growing gaps but if you've made it up to here I'm sure you'll be able to fill in

those details yourself. Here are a couple of super cool facts that can be shown in

the same way. First even when interpreted as base 2, 3, 4, etc., Liouville's

monster will always be a transcendental number. Second even when we replace the

ones by other digits we get a transcendental number as long as

infinitely many of these digits are nonzero. Now adding an integer to a

transcendental number gives a number that is still transcendental. Maybe

someone prove this in the comments. So adding 5 to the transcendental

number up there give a new transcendental number: five point one two zero,

zero, zero, and so on. Here's a fun idea then. Let's take a real

number like pi and use its digits to create a new number like this. Well

it is super-tough to prove that pi is transcendental whereas proving the

transcendence of this weird clone is not any harder then what I've showed you

earlier. Ok, next trick. Let's do the same for

every real number. What this does is create a clone of the set of real

numbers within the set of real numbers. It consists entirely of transcendental

numbers. Even the clones of the algebraic numbers are transcendental. We just have

to be a little bit careful here when we translate a number that features a

terminating decimal expansion like for example the number 1.23.

Using that terminating decimal expansion would also result in a clone with a

terminating decimal expansion and any number like this is rational and

therefore not transcendental. Of course that is easily fixed because every number

with a terminating decimal expansion has a second decimal expansion with an

infinite tail of nines for example 1.23 is equal to

1.2999..., and so on. Using this alternative decimal

expansion which features infinitely many nonzero digits will then give a

transcendental clone. Well one mini problem remains: the number 0 cannot

be massaged in this way to give a transcendental number. But, okay, as it

happens, quite often 0 is a little exception here, big deal. Anyway, we now

have got a clone of the real numbers within the real numbers consisting of

transcendental numbers. Of course, since it is a clone, there is a one-to-one

correspondence between it and the original set. In other words, just like

the real numbers the clone is an uncountably infinite set. But, of course,

in addition all its elements are easy transcendentals super cool, right? However,

this uncountably infinite set also has the paradoxical property of having

measure zero. So although it is as large as the whole set of real numbers, it is

so well hidden within that in a sense it's not even there. To really be able to

appreciate this paradoxical set you should watch the previous video where I

also give a little intro to how you can assign a length or measure to a subset

of the real numbers, or you could head over to Infinite

Series where Kelsey is also discussing these sorts of sets at the moment. I've

also prepared a proof of the fact that the clone has measured zero but I think

this video is already getting quite long and so I'll put this proof on Mathologer 2

sometime in the next couple of days. Okay, let's finish here. I hope you all

understood and enjoyed this video. But, as usual, please let me know what worked for

you and what didn't and if you are struggling with anything just ask. And

that's it for today. [Music]

For more infomation >> Liouville's number, the easiest transcendental and its clones - Duration: 20:40.

-------------------------------------------

Christopher Martin Presents James Longstreet (Homeschool Connections) - Duration: 2:48.

Hello, my name is Christopher Martin. I will be teaching several classes for

Homeschool Connections in the coming school year. If you're curious about the

sort of material mind encounter in my class, I'd like to share a story with you.

Let me introduce James Longstreet, a Confederate General in the Civil War.

Generally, when we talk about Confederate generals, two main figures come to mind.

Robert E Lee the Commander of the Army of Northern Virginia and Thomas Jackson

one of Lee's corps commanders often called Stonewall Jackson. If for all

their acclaim it seems odd that Longstreet usually isn't mentioned with

Lee and Jackson. You see Lee usually left battle tactics in the hands of his corps

commanders, Jackson and Longstreet. And while that explains Jackson's fame, Lee

actually went out of his way to make Longstreet the Senior Corps Commander.

That means that Longstreet, not Jackson, was Lee's most trusted subordinate and

second-in-command. Indeed, Longstreet's performance in the war certainly merited

attention. His stellar defense at Fredericksburg was beyond threat and his

attacks at second Bull Run, Manassas, Chickamauga, and the wilderness, nearly

destroyed the opposing army. So then why don't we hear so much about Longstreet?

Well, first of all Longstreet felt the best thing for southerners to do after

the war was to ally themselves with the party in power, the Republicans. Most

southerners despised the Republican attempts to create racial equality and

saw the Republicans as vindictive tyrants. Longstreet's alliance with the

Republicans even accepting a government position from his friend President Grant

branded him a traitor to the south. Secondly we need to remember that the

Civil War occurred in the wake of the Second Great Awakening with the result

that many people including Lee in Jackson often spoke of God in an

emotional impassioned way. Longstreet however became very reserved after a

personal tragedy in the winter of 1862 when three of his children aged eleven, four,

and one all died of scarlet fever. Catholicism's emphasis on the inner

spiritual life and the lack of political biases and the Catholic views attracted

him and he converted in 1877. To southerners who already questioned

Longstreet's character this conversion made him not just a traitor but also an

apostate. After the Civil War southerners quickly

latched on to Lee and Jackson and their cultural icons when they largely wrote

Longstreet out of their history. The end result is that we have not only

heard more about Lee and Jackson than about Longstreet but we also have a much

better understanding of how the South treated Catholics and friends of black

civil rights in the Reconstruction era. Again, I'm Christopher Martin and I hope to

see you again soon.

For more infomation >> Christopher Martin Presents James Longstreet (Homeschool Connections) - Duration: 2:48.

-------------------------------------------

How To Get Rid Of Blackheads In 3 Minutes - Duration: 1:29.

OUR WEBSITE : http://justhealthrelated.com/

HOW TO GET RID OF BLACKHEADS IN 3 MINUTES

"Open comedo" or blackheads are almost everyone's problem.

They are under the skin, especially around the nose.

They aren't any health problem but they look ugly and dirty.

And it is mainly dirt and oil under the skin.

Today we are going to present you some natural home remedies that can help you to remove

the blackheads from your skin.

INGREDIENTS

Cinnamon powder (1 tbsp.)

Honey (1 tsp.)

Cotton balls INSTRUCTIONS

Prepare a paste from the cinnamon and the honey by mixing the two of them.

Apply it on the blackheads.

Apply the cotton ball for 3 min. and then the blackhead will stick on the cotton ball.

Wash your face and apply a cream.

REMOVING BLACKHEADS IN A FEW MINUTES

Put 4 drops of honey on a lemon sliced into half and rub your face with it.

Leave it for 5-7 minutes and then wash your face.

The honey is a natural moisturizer and the lemon reduces all types of spots on your face.

The results will be visible after 1-2 weeks.

REMOVING BLACKHEADS IN 15 MINUTES

Here is one more homemade remedy for blackheads.

INGREDIENTS

Milk (2 tbsp.)

Unflavored Gelatin (1 tbsp.)

PREPARATION

Mix the ingredients and put them in the microwave for about 10-15 second.

When the mixture will cool down apply it on the blackheads.

Leave it for 15 minutes and peel it off.

Don't Forget To Follow Us On Other Social Media :

INSTAGRAM: http://bit.ly/2m7bnd1 FACEBOOK: http://bit.ly/2kYKuD0

TWITTER: http://bit.ly/2l74mVA PINTEREST: http://bit.ly/2lEUYvn

Subscribe our channel for more!

For more infomation >> How To Get Rid Of Blackheads In 3 Minutes - Duration: 1:29.

-------------------------------------------

Top 10 Amazing Cakes Decorating Ideas 🍰 Cake Style 2017 | Most Satisfying Cake Decorating Videos - Duration: 10:11.

Thanks for watching

Hope you have a great time

Please, like, comment and subscribe for more!!

For more infomation >> Top 10 Amazing Cakes Decorating Ideas 🍰 Cake Style 2017 | Most Satisfying Cake Decorating Videos - Duration: 10:11.

-------------------------------------------

Alan Alda | Your Biggest Fan - Duration: 3:14.

For more infomation >> Alan Alda | Your Biggest Fan - Duration: 3:14.

-------------------------------------------

Painted By Zeeshan | Unique Stories From India - Duration: 4:55.

Tap the bell icon on YouTube app

And never miss out on unique stories from 101India

I have always been very free of norms and regulations

When it comes to it

I am into make up and costume

I'm into styling

I'm into creating magic, eventually

My name is Zeeshan, I'm 24 years old

I'm basically from Mumbai

But I have shifted to Bengaluru

I'm doing my college over there

I have always been open about my lifestyle

And my personal choices

Everyone is unique in their own specific way

I realised very early that I was different and unique

My mom is my inspiration

My love, my first lady in my life

She means the world to me

I tear up when I speak about her

Whenever my daughter or I dress up

He would advise us on how to wear it

Makeup is in fashion these days

Everyone does it, whether it's a boy or a girl

My parents have always been supportive of me

Like, when I wanted to shift from medical to fashion

Which was a big change

When I did that shift, I hadn't spoken to them about it

For a year

And I was scared that they wouldn't accept me

But they were very supportive of me

And my life choices as well

I used to love being photographed

That has always been a part of my life

And I really enjoy that

When I went to Bengaluru, a friend of mine approached me

To do an androgynous shoot

I was like, sure!

That is something I would love to do

I started clicking photos of myself in different forms

Just a year back

Make up is all self taught in a way

I started playing around with it

There is so much of material online

To figure out what you want to do and how you want to do it

Most of my photos have been shot by me

Proper timing and lighting is required

I generally keep my phone on timer

So it's easier for me to pose and click

And then it goes on Instagram and Facebook

I generally don't design a look

I look at the colours and pieces that I make

It's very random in that way

At times, I have an inspiration

I love playing with things which might look f**ked up

In reality

But in (the final) avatar, it comes through

It's like 'Oh my god!

What is this?'

I had this bra

I glued beautiful synthetic wool in pink and green

It was like an alien fly kind of a thing

Sourcing, looking at the materials and feeling them

That's how my process starts basically

I love street shopping

That's something that has always interested me

I did one with the doormats

My cat was the inspiration for this

For this one, I made the mould for my face out of gelatin

To give a reptilian texture and scale effect

I want to be the face of a make up company

Because, why not?

It's high time a boy in India is the face of a brand

I want parents to know that if their kids

Want to do something new, something good

One shouldn't stop a flowing river

I have learnt so much along the way

Gained so much confidence along the way

I am enjoying it

It's something I look forward to doing everyday

I wake up in the morning and think

What am I going to do today for a look

This is how I live, basically

It's never ending and it will never stop

For more infomation >> Painted By Zeeshan | Unique Stories From India - Duration: 4:55.

-------------------------------------------

THIS THURSDAY - Talking Tom and Friends | Season 2 Episode 2 (Sneak Peek) - Duration: 0:31.

Avoid Angela...

And I'm done!

How could Tom stand me up like this?

It's like my heart is on an elevator that's going down and Tom pressed all the buttons!

Hi Angela...

For more infomation >> THIS THURSDAY - Talking Tom and Friends | Season 2 Episode 2 (Sneak Peek) - Duration: 0:31.

-------------------------------------------

5 Signs Of Colon Cancer We All Ignore For Years - Duration: 1:06.

OUR WEBSITE : http://justhealthrelated.com/

5 Signs Of Colon Cancer We All Ignore For Years

This type of cancer is very often and if found in its early stage treatable.

Only in 2016, 140 000 people had colon or rectal cancer.

There are a few signs that can signal a colon cancer.

CRAMPS

If you have some sort of cramps that doesn't mean that you have cancer but if those symptoms

last for a longer period of time, then probably the best thing to do is visit your doctor.

FATIGUE

In this modern society we are all constantly tired and under stress but don't overlook

this symptom because cancer can make you tired and fatigue too.

WEIGHT LOSS

Strangely losing weight is 5% of your total weight in few months.

So pay attention to your weight and if you are losing it strangely without changing any

of your everyday routines.

IRREGULAR BOWELS

This is one more thing that you must pay attention to, the consistency, timing, and appearance.

Another thing that can change your bowels are polyps but the best thing to do is pay

a visit to the doctor's office.

Don't Forget To Follow Us On Other Social Media :

INSTAGRAM: http://bit.ly/2m7bnd1 FACEBOOK: http://bit.ly/2kYKuD0

TWITTER: http://bit.ly/2l74mVA PINTEREST: http://bit.ly/2lEUYvn

Subscribe our channel for more!

For more infomation >> 5 Signs Of Colon Cancer We All Ignore For Years - Duration: 1:06.

-------------------------------------------

Find the odd appearing element in O(Log n) time | GeeksforGeeks - Duration: 5:11.

For more infomation >> Find the odd appearing element in O(Log n) time | GeeksforGeeks - Duration: 5:11.

-------------------------------------------

After I Started Drinking This I Never Got Fat Again! I Only Used 2 Ingredients - Duration: 0:47.

OUR WEBSITE : http://justhealthrelated.com/

After I Started Drinking This I Never Got Fat Again!

I Only Used 2 Ingredients

Flaxseeds are full of vitamins, fatty acids, minerals, and fiber.

They are good for losing weight, for our overall health, and digestion.

They regulate our blood sugar, help with indigestion, and detoxify our body.

Another benefit from them is that they boost the metabolism and reduce the fat in the body.

Today we are going to present you a home remedy with flaxseeds.

INGREDIENTS

Flaxseeds (3 tbsp.)

Boiled water (1 l.) PREPARATION

Pour the boiled water over the seeds and let they stay over the night.

Drink this the next day.

You should drink this for 10 days for better results.

Don't Forget To Follow Us On Other Social Media :

INSTAGRAM: http://bit.ly/2m7bnd1 FACEBOOK: http://bit.ly/2kYKuD0

TWITTER: http://bit.ly/2l74mVA PINTEREST: http://bit.ly/2lEUYvn

Subscribe our channel for more!

For more infomation >> After I Started Drinking This I Never Got Fat Again! I Only Used 2 Ingredients - Duration: 0:47.

-------------------------------------------

No Diet, No Exercise. This Remedy Will Flatten Your Tummy In Just 1 Week! - Duration: 1:01.

Visit Our Website Here : http://bit.ly/2q90Dxh

NO DIET, NO EXERCISE.

THIS REMEDY WILL FLATTEN YOUR TUMMY IN JUST 1 WEEK!

We are going to present to you in this article a simple solution that works 100% against

belly fat.

This remedy is so great that will help you reduce the fat around the belly area in very

short period of time.

Also it doesn't require strict diet or regular exercising.

You will need to consume this remedy for one week in order to reduce the weight and eliminate

unwanted belly fat.

Here is how to prepare it:

Ingredients:

Lemons – 3 Water – 4 cups

Rock salt – a pinch First you will need to cut the lemons on half

and extract the juice in a bowl.

Keep the peels aside because you will use them as well.

Next, boil the water and add the remaining ingredients.

Lower the heat and leave it for 5 minutes.

After it is done put it in a bottle and consume it after your meals.

Remember that you should never consume this remedy before your meal.

Thank you For Visiting Our Youtube Chanel Please don't forget to subscribe our channel

Subscribe : http://bit.ly/2rRgSLG

For more infomation >> No Diet, No Exercise. This Remedy Will Flatten Your Tummy In Just 1 Week! - Duration: 1:01.