Your "proofs" simply assumes that 0.999... is a notation denoting 1, without exa... | Hacker News

Hacker Newsnew | past | comments | ask | show | jobs | submit

		kazinator on Sept 3, 2016 \| parent \| context \| favorite \| on: The Math Myth Your "proofs" simply assumes that 0.999... is a notation denoting 1, without examining the underpinnings which might legitimize that. 9.999.. - 0.999 is 9 no matter how we define .999... just as long as two or more occurrences of the 0.999... notation all denote the same entity, and we understand that the syntax 9.999... is 9 + 0.999... For example, if we define 0.999... as "rubber duck" then 9.999... stands for 9 + "rubber duck", and 9.999... - 0.999... stands for 9 + "rubber duck" - "rubber duck" = 9.

iopq on Sept 4, 2016 | [–]

While that's true, the whole key to the proof is that

0.999... * 10 = 9.999...

Because "one less 9 than infinity is still infinity" it's what really closes the loop on the proof.

Guidelines | FAQ | Lists | API | Security | Legal | Apply to YC | Contact