You are reading a single comment by @frankenbike and its replies.
Click here to read the full conversation.
-
By ^ do you mean up arrow (↑) or exponent?
Either way I think you've vastly underestimated it:
3↑↑↑3 is 3↑↑(3↑↑3) which is 3↑↑(3²⁷). So a power tower of 3s that is 3²⁷ long.
G1 is 3↑↑↑↑3 = 3↑↑↑(3↑↑↑3). That is 3↑↑(3↑↑(3↑↑(3... this series of numbers is 3↑↑↑3 long and a ↑↑ operation is basically a power tower. At the end of the sequence, you've got 3²⁷, then you form a power tower that is 3²⁷ long, then a power tower that is that long, and so on. You repeat this 3↑↑↑3 times...
G2 is a 3 followed by G1 arrows and then 3. Graham's number is G64
frankenbike
jj72
Maths wizzes:
I’m trying to convey/‘comprehend’ how massive Graham’s number is, by explaining the first steps to calculate it. Is the following correct?
G=g64
3 ^ 3 ^ 3 ^ 3 =
3 ^ 3 ^ 27 =
3 ^ 7,625,597,484,987
g1= 3 ^ (3 ^ 7,625,597,484,987) in a tower (3 ^ 7,625,597,484,987) high?
g2= g1^g1^g1.... creating a tower of ^g1 that is (result of power tower #g1) high?
And so on for g3, g4, and all the way to g64?
Edit- explaining in laypersons terms to other laypeople, leaving aside strictly correct notation. Edit2 with what I think is a corrrction having read the wiki page (missed a tower).