Name: TREE vs グラハムのナンバー - Numberphile (TREE vs Graham's Number - Numberphile)
Uploaded: 2021-01-14T10:16:43.000Z
Duration: 23 min 50 s
Description: VoiceTubeの動画で発音を聞きながら英語表現を覚えよう！学べる英語：

So you remember in the past tweeted and we don't to really big numbers in particular in the past with Graham's number and tree three.

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So you remember Tree three was this number that was that was so big that even just to prove that it was finite, there just wasn't enough time left in the universe.

To do that, you would have a universal to reset itself before you ever got to complete the proof.

Grand Name was so big that if you thought about it, your head would collapse to form a black hole.

But what I really want to talk about today is kind of crazy of crazy.

I want to talk about On Over, which combines both on that's tree of Graham's number.

I'm worried the universe is gonna collect way.

As you might remember from from those original videos, both tree three on Graham's number, they both the rises in sort of a sequence ticket.

Let's let's remind ourselves what where Graham's number came from, sort of very briefly to get to Graham's number.

We started out with something which alcalde G one, which was three arrow, arrow, arrow, arrow three.

Now, just to remind you what these arrows were, if I have three arrows three, that just means three to the three.

It's a fancy way of writing three to the par three, which is of course, 27.

If I take a double arrow, Well, that just means doing a repetition of the single arrow.

Three times that would be three arrow three, arrow three, which is three to the Arrow 27 which is about 7.6 trillion.

And then if you had three arrows, well, that's just repeated double arrows.

Okay, so that's just repeat repetition of the double arrow.

So that's three to the three to the three, which is again three double R A.

7.6 trillion, which is basically a power tower of three.

Is this is just stupidly big numbers on actually, the first sort of wrong on the ladder of Graham's, Graham's flat little rain sequence is actually has four hours, so it's a repetition of three hours.

So this is the first point on grand sequence, but then you go up.

Graham told us to do was actually to sort of build this sequence, or he would then go to G to where the number of arrows itself was already this huge number.

Okay, so you actually now have G one arrows on the arrows.

As you can see from this making it was really, really big toe, actually.

Now, when we start putting really big numbers in the number of arrows, we get crazy big.

And he carried on with this sequence until you got to G 64.

So you have this sequence one start for this G one due to until all way up to G 64 you can carry on right.

This defines the sequence which you could call G n, which is basically related to the one before by taking the number of arrows that you had before.

The tree trees also gave to see who's never remember from that video.

The trees are basically is this idea of you play a game with with a finite number of seeds, different types of seeds and you try to grow trees.

And the idea is, how long can this game go on for?

So if you have one type of seed, then the game can last a maximum off.

So if you have two different seeds, is three and then if you have three different seeds, then the game literally goes on for potentially gone for absolutely ages.

It's actually bigger than grains that but that's what I told you.

Okay, so we're gonna think a bit more about that.

But this is a truly truly gargantuan number on dhe.

But of course, you could carry on with this sequence.

You could try tree 43536 in general, some tree end.

And you could even think, of course, about tree of Graham's number.

The real question I want to ask you is Which sequence is better?

We've got these two sequences we got tree event on.

OK, we can build this number tree of Graham's number, right, which is basically Tree of G of 64.

But I could also think about going the other way around.

I mean, do the trees first and then do the G's seven other ways.

I'm going to start playing the game of trees first and then I climbed grams ladder.

I mean by that I mean take tree in this case of 64 on, then evaluate that Ingraham secrets.

So here I am, climbing grand ladder 1st 64 rooms on.

I'm playing the game of trees with 64 instead of seeds.

I got the impression from you in the previous videos that trees are more powerful, so I'm going to say that one's bigger.

Yeah, but it's you're giving the tree less juice there.

You're only giving the tree 64 juice and there you're giving the tree Graham's number.

Do I think that's a beautiful way to put it actually ready.

But let's let's actually explore this a little bit more.

Let's do with a much simpler, simpler pair of sequences which are basically just powers.

So I can imagine sequence where p to the end is to to the answer, basically take take the 22 to the power of whatever number I'm interested in on quadratic ce.

If you give me an I give u n squared just two different secrets the night of these anywhere near as powerful as tree or G.

But they'll they'll illustrate the point now, as you would put it in this case, the exponents.

Okay, this is more powerful than a quadratic exponents grow more quickly than quadratic ce in this case, we could study and asked which is it better to do first or last?

Okay, which is gonna take us to the bigger place?

And let's let's start with maybe an equals one.

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TREE vs グラハムのナンバー - Numberphile (TREE vs Graham's Number - Numberphile)

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