9th grade math question

Please bear with me if I am not following a protocal for the group.

My step daughter is in 9th grade math (she is in 7th grade).
She asked me earlier in the week if .999 going off in to infinity is the 
same thing as 1.

I said no.  Close...but no.
I am by far no pro at math.
She insists its the same, because her math teacher said so...

But, I do seem to remember a math teacher telling me that mathmatically,
it 
can be the same as one.  In reality it is not.  He told me to think of two

lines.  To be parallel, the need to be the same distance apart...say 1. 
If 
they are .999999 apart...eventually they will meet.  And, no matter how
far 
out you go in to infinity, you still will not reach 1.
Best I can think of is that this is a mathmatical concept, that exists on 
paper....
Can anyone here give an answer that makes sense to me, or her?
Thanks....