[yongjik]

TLDR: It is a rather nontrivial result that each real number can be represented by an infinite sequence of digits, although not uniquely (as other comments said).

However, to understand that, we need to answer several questions:

* What is a real number, after all? How do we even define it?

* When we have a sequence of digits like 0.12345678..., and when we say this sequence represents a number X, what exactly does that mean?

* (...which leads to): What is a sequence? What does it mean for an infinite sequence to converge?

So, it's definitely not "Duh, it's obvious": some work is needed to understand all this. I recommend reading the first several chapters of any good book on analysis.

[sillysaurus3]

If you write the first digit of pi after one minute, then the second digit after 30 seconds, then the third after 15 seconds, then the fourth after 7.5 seconds, and so on...

What's the last number you've written after two minutes? Is it the last digit of pi?

[Smaug123]

Huh? There isn't a last number you've written after two minutes. You've written them all, but there's no terminating one.