What is the biggest number known to man kind?

Answer 1

It's graham's number

I recently had the pleasure of meeting Graham's Number, the Guinness Record largest named number -- one with a "practical" purpose, anyway, its being used in a mathematical proof.

It is shown to be an upper bound on a not unreasonably stated word problem (and it also relates to the coloring of the corners of hypercubes of dimension n, but that's so hard to picture):

"Take any number of people, list every possible committee that can be formed from them, and consider every possible pair of committees. How many people must be in the original group so that no matter how the assignments are made, there will be four committees in which all the pairs fall in the same group, and all the people belong to an even number of committees."

Some uncommon notation is need to express it with a formula. Just as multiplication is a generalization of addition, and exponentiation is a generalization of multiplication, the arrow function is a generalization of exponentiation.

For instance:

3↑3 is the ordinary 3-cubed, 27.

3↑↑3 is 3 raised to (3 raised to 3), 3↑27, a good-sized number, 7,625,597,484,987.

3↑↑↑3 is 3↑↑(3↑↑3), or 3↑↑7,625,597,484,987, a very large number. That is: 3 raised to (3 raised to (3 raised to...)))

7,625,597,484,987 times.

3↑↑↑↑3 is 3↑↑↑(3↑↑↑3). Big. Very big.

Still with me? 3↑↑↑↑3 is the starting point for defining Graham's number.

G1 is 3↑↑↑↑3.

G2 is 3↑↑...G1 total arrows...↑↑3. Yikes! But, we've only just begun.

Generally, Gn is 3↑↑...Gn-1 total arrows... ↑↑3

Finally, Graham's Number is G64. That is: 3↑↑...G63 total arrows...↑↑3. It makes me feel woozy. I think I'm gonna hurl.