User talk:Clive tooth

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Hello, 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: Please remember to sign your messages on talk pages by typing four tildes ( ~ ); this will automatically insert your username and the date. If you need help, check out Questions, ask me on my talk page, or ask your question on this page and then place  before the question. Again, welcome! RJFJR (talk) 14:02, 19 July 2013 (UTC)
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Just made another modification to the final entry at Timeline of the far future
Is my math up to snuff? :)  Serendi pod ous  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)