On Fri, 8 Sep 2017 11:01 pm, Rhodri James wrote:
> On 08/09/17 13:45, Stefan Ram wrote:
>> Gregory Ewing<greg.ew...@canterbury.ac.nz> writes:
>> [a random integer will on average have ]
>>> infinitely many
>>> digits -- despite every actual integer only having finitely
>>> many digits!
>> This is not possible because every integer has
>> a finite number of digits (in base 10).
>
> Surely an infinitely large integer has an infinite number of digits?
There are no infinitely large integers. All integers are finite.
We can say that there is no largest integer, that they go on forever -- but no
individual integer is infinite.
We soon run out of notation to write them. There are numbers so inconceivably
huge that ordinary exponential notation isn't big enough, like Graham's Number,
and we can invent numbers even bigger:
let G = Graham's Number
let H = G^^G^^G^^ ... ^^G # tower of a Graham's Number G's, where
^^ is the tetration (double arrow) operator:
x^^y = x^x^x^...^x # tower of y x's
but even those inconceivably huge numbers are finite.
That's the thing about infinity. No matter how huge the number is, it is still
falls infinitely short of infinite.
--
Steve
“Cheer up,” they said, “things could be worse.” So I cheered up, and sure
enough, things got worse.
--
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