Re: #308 decimal representation of Infinite Integers such as 9876.....54321; new textbook: Mathematical Physics (Reals & Counting Numbers/AP-adics Primer) for age 6 years onward

a_plutonium <a_plutonium@xxxxxxxxxxx> writes:

But I am telescoping in on the correct notation.

We can think of 10^2 as that of 0000.....00000100
And 10^3 as that of 00000.....0000001000

So that 10^9999......999999 is 100000.....00000
and 10^9999....99998 as 01000000.....000000

So again I made a mistake in my previous post concerning the number
9876.......54321

That number in proper Infinite Integer decimal notation is this number

9 x 10^99999....999999 + 8 x 10^9999....999998 + 7 x 10^9999.....99997
and so forth

And so, we have

10^1 > 1
10^2 > 2
10^3 > 3

and so on, but

10^999...999 = 1000...000 < 999...999.

So there must be some number n such that

10^n > n

but

10^{n+1} < n.

Which number do you think that is?

Thanks.

--
Jesse F. Hughes

"The three principal virtues of a programmer are Laziness, Impatience, and
Hubris."-- Larry Wall in the Perl5 Manpages
.