Close enough

I ran across an interesting tidbit that I missed during my years in school.   Apparently 0.9̅ = 1.  (If you can't see the special character, the 0.9 is repeating, meaning 0.9999999...)  I initially didn't believe it either, since I, too, thought of this number as something approaching the limit of 1.    It turns out that you have to think harder about the nature of infinity in order to get your definitions right.   What helped me is this:  how small is the difference between 0.9̅ and 1?  It's infinitely small, or 0.

From Wikipedia:

"The equality 0.999... = 1 has long been accepted by mathematicians and is part of general mathematical education. Nonetheless, some students find it sufficiently counterintuitive that they question or reject it, commonly enough that the difficulty of convincing them of the validity of this identity has been the subject of several studies in mathematics education."

Link to article...

Also, the best part:

"Q: How many mathematicians does it take to screw in a lightbulb?"
"A: 0.999999...."