Graham's Number - Literally head-imploding

[Shortcut]

Where are you stuck? if it's the arrows, I don't fully understand them either.

haha i was just making a joke

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[Legodude77]

It's simple then, we find a way to implant thoughts in our heads, put this number inside someone's head, and then get power somehow from the black hole produced!

[TheKhoz]

That Numberphile is like a year old...

I'm just confused, because I assume that most people are subscribed to Numberphile.

[Nickelob Ultra]

This number is literally so big that you would actually turn into a black hole; if you thought about it until the amount of knowledge inside of your brain made it massive enough to form a singularity and collapse inside of itself into a point where light could not escape.

pics or it doesnt happen

[Axo-Tak]

TREE(3) is way larger than Graham's number. Also, since TREE(x) is a function with an enormously fast rate of growth, I'd imagine that TREE(4) would require special notation that would be complicated tenfold.

The mathematician Harvey Friedman observed a special finite form of Kurskal's Tree Theorem. Regarding this form, Friedman discusses the existence of a rapidly growing function he calls TREE(n).

The TREE sequence begins TREE(1)=1 and TREE(2)=3, but TREE(3) is a number so extremely large that its weak lower bound is (A(...A(1)...)), where the number of A's is A(187196), and A() is a version of Ackermann's function: A(x)=2↑↑...↑x with x−1↑s (Knuth up-arrows).

Whereas Graham's Number is A⁶⁴(4), the above mentioned lower bound is AA(187196). As you can imagine, the TREE function keeps on growing rather quickly. For a discussion on the hierarchy of fast growing functions see here: http://en.wikipedia.org/wiki/Fast-growing_hierarchy

There are other examples of numbers greater than Graham's Number, as can be seen here: http://en.wikipedia.org/wiki/Goodstein_function#Sequence_length_as_a_function_of_the_starting_value, although I'm not sure if this number is larger than Friedman's TREE(3)

[Treynolds416]

I mean, I thought most people had heard of graham's number...

[skill4life]

pics or it doesnt happen

[Bloody Mary]

Graham's Number is not noteworthy because it's head-imploding, it's noteworthy because it's one of the few head-imploding numbers that is actually used for something constructive. There are literally an infinite amount of head-imploding numbers: Graham's Number is not special in that regard.

Also, as a side note, I think you can use a carat (^) instead of those awkward arrows; they are more commonly used and can be typed much easier. I could be wrong about that but I don't think I am.

edit: Turns out the arrows are for implied repeated multiplication or something. I think. I'm not sure why they do it but I don't presume to know more than mathematicians. Disregard the above sentence.

[Kingdaro]

TREE(3) is way larger than Graham's number. Also, since TREE(x) is a function with an enormously fast rate of growth, I'd imagine that TREE(4) would require special notation that would be complicated tenfold.

Well that escalated quickly.

[Pacha-]

Graham's Number is not noteworthy because it's head-imploding, it's noteworthy because it's one of the few head-imploding numbers that is actually used for something constructive. There are literally an infinite amount of head-imploding numbers: Graham's Number is not special in that regard.

Also, as a side note, I think you can use a carat (^) instead of those awkward arrows; they are more commonly used and can be typed much easier. I could be wrong about that but I don't think I am.

edit: Turns out the arrows are for implied repeated multiplication or something. I think. I'm not sure why they do it but I don't presume to know more than mathematicians. Disregard the above sentence.

yeah, aren't carats used for exponents ie. 6^3 = 6³ ?

[Bloody Mary]

yeah, aren't carats used for exponents ie. 6^3 = 6³ ?

Yes. It's because when you type it's not convenient to write a number above your own to indicate exponential multiplication; the carat is a way of showing that the number after it is above the first number by about half a line's worth. In real life you can just write a little bit above the number, so if you use a carat to indicate an exponent you'll probably get laughed out of your math class or something.