Name: All the Numbers - Numberphile
Uploaded: 2020-03-27T17:47:57.000Z
Duration: 14 min 27 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

we're gonna do A ll the numbers on number five.

We've done a lot of the numbers, some would say, but we haven't done all the numbers.

Adverbs of manner

Originally, we did the whole numbers and these are the classics.

But then there are other types of numbers.

If we go one, step out the Russian ones, the ones that are ratios, these air, you know, you get 17th you get I don't know things over 12.

The rational numbers we've gone beyond that day on the rational technically include the whole numbers.

But I'm doing this as what people call Venn diagram, which is wrong.

A diagram showing every single possible combination, negative numbers, whole numbers.

You know, I put in the 12th because I thought I was being hilarious.

And then I immediately thought I wasn't gonna put negatives on this diagram.

So I regret that for two reasons opening the negative can and the expression on your face.

So I'm gonna make that a plus that we are.

In fact, this whole sheet of paper is just gonna be the reels.

And inside here, I've put whole numbers and then I put rational numbers.

If you can obviously get complex numbers coming up, we're not gonna do that.

We're going to stay down here and I'm gonna raise We work our way out until we get a greater distance out.

The number five has ever gone before, right?

We're going for the new number file record.

But we're done rational next one up, the constructive ALS and these often aren't mentions.

You don't have to add this in as a category, but I quite like constructive ALS Maur.

People tend to go for the next one out of the algebraic.

Okay, so Simon did a fantastic video about algebraic numbers.

And when you go outside, transcendental numbers mean this number is really, really important.

No one you and so a lot of the number categories referred to in or out off these different sets.

So rational numbers or everything inside the blue line, irrational numbers or everything outside the blue line.

You've got constructively numbers or anything inside the Purple line.

All numbers are outside this and this light blue line out here.

Algebraic numbers, everything inside there and transcendental numbers, everything outside of them.

All numbers are things that you can construct with a pencil and a compass and a ruler so fi you can do that.

The golden ratio because you can do Route five so you can get five you can do route to that lives in here is kind of fun.

Algebraic numbers are the solution to an algebraic equation.

If it's a square root or lower, you can put in constructively.

You can draw it if it's high in that you can't.

So the cube root of two isn't algebraic number, and then outside algebraic.

So you got things like Pi Pi lives out here.

That's out there, things that are a nice, neat solution to another break equation.

I let they're out there right This is how people tend to categorize all the numbers.

This is the fringe of kind of what we understand in mathematics and what we've done on number file.

So he was the first number that was proven to be transcendental.

And so that was proven in 18 73 so reasonably recent, given that some of these of thousands of years old we knew existed but didn't know where it went pie.

80 to so hee to the power of pie was proven to be out here in only 1934.

Messed approved is out there and there are loads which we don't know pi to the A.

We don't know each of the we don't know pi to the pie.

We know that one off e times pi or e plus pi.

One or more of those a transcendental we don't know which or both, right, But, you know, at least one of them is most numbers that we know are algebraic.

Sit around here and we don't know if they're definitely transcendental or if they're still on your break.

For the most part, we haven't got a clue, right?

If you look at the entry for transcendental numbers on Wikipedia or Math World, this is a list.

Here's the only ones we know And that's it, right?

But they're also infinitely many rational numbers.

Many construct herbal numbers, imaginary numbers, but a ll countable infinity is the smallest infinity possible.

Many off these numbers in here and there is one more circuit out, you know, what should we check on the last one?

I can add another loop and it cleans up all of these and it puts the ball in a neat bow.

This is the collection off computer poll numbers, computer.

That means we can compute them so we can compute.

It's not the solution to a nice equation, but I can write down a system by which you will get the decimal place right?

We print them out on a very long bit of paper rolling out on runway.

We're here on a runway because for some reason, Brady has printed out the 1st 1 million digits off pie.

This came down to Alan cheering in 1936 and even remembers that sharing invented the computer with the Turing machine.

And that was in his paper on computer ble numbers he was looking at If you can compute all numbers and he showed their number that exist out here, but we just don't know what that I called the dark numbers right?

All these numbers that we know they exist.

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All the Numbers - Numberphile

weird

incredible

hilarious

insane