Are all infinity’s the same?

Question

If 1/infinity = .*infinite 0s*1 and .999repeating are added together do they arrive at 1?

I was told 1/infinity times 1 = 1/infinity

I was also told .999repeating = 1

As X=.999repeating

10X=9.99repeating minus

X=.999repeating =

9x=9

x=1

From which I gathered if it is possible to subtract infinity’s, wouldn’t the opposite also be true?

(.9repeating) plus

(.repeating 0s then 1 at the end)

equals ???

Answer 1

You need to do some reading.

The concept of infinity is a difficult one and holds many non-intuitive surprises.

You need to ask about Dedekind cuts and the sense in which .999999.... is said to = 1.

You probably should also look at least at some simple descriptions of work done by G. Cantor.

You should also find out about so-called infinite sequences and infinite series.

Once you understand some of that you will be able to answer your questions...and probably not before.

Good luck and good reading!