Clive tooth
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editHello, Clive tooth, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few links to pages you might find helpful:
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Just made another modification to the final entry at Timeline of the far future
editIs my math up to snuff? :) Serendipodous 12:57, 13 April 2016 (UTC)
- Yes, your maths is fine. 10^10^10^56 is such a vast number that just multiplying it by any number smaller than it leaves it pretty much the same. In fact we can go much, much further...
Let us give 10^10^10^56 the name K. As far as the "Timeline of the far future" is concerned, the next "number of interest" after K is, I suppose, 10^10^10^57.
As you probably know 10^100 is usually called a googol. What happens when we raise K to the power of a googol? That is, what is K×K×K×K× ... ×K where there are a googol Ks?
Let's see...
Let A = K^googol = K^(10^100) = (10^10^10^56)^(10^100) = 10^((10^100)×(10^10^56) = 10^10^(100+10^56)
That is, the 10^56 in the definition of K has (for A) been increased by just 100, to 10^56 + 100. Still an enormous way from our next "number of interest" 10^10^10^57.
In other words
K = 10^10^100000000000000000000000000000000000000000000000000000000 [a 1 followed by 56 zeros]
And K^googol = 10^10^100000000000000000000000000000000000000000000000000000100 [where the 54th zero has become a 1]
So K^googol = K, as far as we are concerned. :) --Clive tooth (talk) 17:28, 13 April 2016 (UTC)