Is 0.999… really equal to 1?

mathema-tricks.blogspot.com

4 pointsmquaes3 comments

The article is quite good, but says, "If we assume infinitely small numbers don’t exist, we can show 0.999... = 1."

What if we use epsilon-delta proofs to show that the limit as the number of digits in 0.999... go to infinity, the number approaches 1?

That's not assuming much; infinitely small _differences_ become zero. One divided by infinity equals zero.

The lack of rigor in your explanation undermines the point you are trying to make. You have definitions in your head that you are not expressing in a meaningful way. Ungrounded intuition just doesn't help when reasoning about infinity.

The non-meaning of "1/infinity" was also discussed recently on HN, if I recall correctly.

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