My friend belives that infinity has an end but we somehow can't reach/count it

My friend belives that infinity has an end but we somehow can't reach/count it

We were discussing wether 0.9999...=1 (basically me trying to prove to her that it is mathematically correct) and her main argument is that the equality is wrong cuz if you add 0.0000...1 to 0.999... then it results in 1 thus it's not the same number. And I was like, obviously not, 0.0000...1 is not a real number since the 0s are infinite, so that means the 1 never existed in the first place. But she declined and said that after the 0s ended then there was the 1. ...

And that's where we are now with this post huh. I feel like it's a infinitely (lol) milder case of an earth flatter haha. If someone in the comments can explain how infinity works Imma show it to her