How can .9999etc. be considered equal to 1 in math?

Factual Questions
1

I always read in mathematics books how
.999and 9 forever actually equals 1, and they don’t mean because you just round it off, either, they really mean it literally equals 1. I can’t understand the thinking here. Also, 2) does this also imply that .8888 etc. equals 9? and so on.
I’m not interested in the practical implications, but in the theory of why they say .999999999
etc. has to be considered equal to 1.

2

Eeeeee.eee! I didn’t know that someone else has taken this up. I just posted this and then going to gen questions I see below my post there is a whole several pages on this. I will look into it now.

3

No problem, don, I’ll close this and refer replies to Why doesn’t .9999~ = 1?

DrMatrix - GQ Moderator