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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
by sounds 15y ago
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.
- Drbble 15y agoThe 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.