In article <email@example.com>, Archimedes Plutonium <firstname.lastname@example.org> wrote:
> --- quoting my previous post --- > Alright in the previous posts I defined a constant-series such as > 1 + 1 + . . +1 with 10^603 terms where all the terms are the same and > this series is especially important since it is the smallest divergent > additive series for it equals the Infinity number 10^603. > > Next I explored what the number N x N x .. x N of the constant > multiplicative series that has exactly 10^603 terms and is equal to > 10^603. What is that number N that satisfies those > conditions? In a sense, asking what is the 10^603 root of > 10^603 ?? And asking if that is a special number, an important number > that becomes visible for the first time? > > Is it a number that is special and its neighbors are not special? Is > it far more important as a root than any other root before it? > > I am hoping that to find infinity borderline can be as easy as finding > the root of a special number, like 10^603. We can see that pi is > special at 10^603 for it has its first three zeroes in a row. But can > we find something special with 10^603 as its root? > --- end quoting my previous post --- > > Now here is the pattern so far for pretending that 2 was Infinity or > that 3 was Infinity and we see that at 5 as infinity the fifth root of > 5 is 1.3.. and not 1.4.. > But the question is what is the 10^603 root of 10^603 and is it going > to be > special since pi has three zero digits in a row there? > > 1.41421 square root of 2 > 1.44224 cube root of 3 > 1. 4 quartic root of 4 > 1.3 quintic root of 5 > > Archimedes Plutonium > http://www.iw.net/~a_plutonium > whole entire Universe is just one big atom > where dots of the electron-dot-cloud are galaxies
Look at f(x) = x^(1/x) for increasing x.
Plot it and see what it looks like. For extra credit: Find its maximum.