Pi is non repeating, but if its infinite wouldn't it eventually HAVE to repeat?

[TriggyQuestion]

I mean, there's only so many single digits, so wouldn't an infinite number eventually have to repeat? an infinite decimal would contain all possible number combinations wouldn't it?

 

[lookagain]

I mean, there's only so many single digits, so wouldn't an infinite
number eventually have to repeat?
an infinite decimal would contain all possible number combinations wouldn't it?

No.

Look at this infinite decimal for an irrational number:

\(\displaystyle .01100011110000011111100000001111111100000000011111111110...\)

It has a pattern as to the zeroes and ones, but there are no continuously adjacent repeating uniform
length blocks of digits.

 

[HallsofIvy]

You are misunderstanding "doesn't repeat". Every rational number, expressed as a decimal, "eventually repeats" means that, possibly, after a long string of digits, we have a block of digits such that the rest of the number is precisely that block repeated over and over again: \(\displaystyle a.b_1b_2b_2... b_nc_1c_2....c_nc_1c_2...c_nc_1c_2... c_n....\). A string of digits that happens to repeat once or twice does NOT qualify as saying the number "eventually repeats".