In article <87ocucFrn3U1@mid.individual.net>, "|-|ercules" <email@example.com> wrote:
> Consider the list of increasing lengths of finite prefixes of pi > > 3 > 31 > 314 > 3141 > .... > > Everyone agrees that: > this list contains every digit of pi (1) >
No, I don't agree, so "Everyone agrees that ..." is false.
The list consists of a collection of integers. Item n on the list are the first n digits of pi, starting from 3 and ignoring the decimal point. So the 1000th item on the list is 31... pi to 1000 places.
There is no one element of the list that contains pi in its entirety. And the reason is because each 'n' represents a FINITE NUMBER. Like 6, or 100043, or a zillion eleven. And on that line we find a zillion eleven digits of pi. But no more!
No one item on the list contains pi in its entirety.
Do you understand that?
What is true is that: if you ask me for, say, pi to a trillion digits, I'll say, "No problem, here it is, it's the trillionth item on the list."
But if you ask me for ALL the digits of pi, I have to say, "Sorry, that's not on the list."