A graphic illustration of 0.999…=1

Apologies, not all of us are able to see straight through to the truth in every case. This argument convinced me (not least because it occurred to me too a few years ago ;) - I hadn't seen it anywhere before at the time, though I'm sure this is because (a) I hadn't spent much time looking, and (b) to those skilled in the art, it is so obvious as to be barely worthy of comment.

If you're simply not convinced by his line of thought (it's hard to tell...), an alternative argument might be: noting that 3 multiplied by one third is 1, consider what that would look like if written out in decimal notation.

(I am sure there are plenty more arguments too, probably much better than mine.)

Not to be that guy, but technically (0.999) = 1 - 10^(-inf).

wait .52 = 1 ? view source "or .5<i>2 = 1 or 1/9 </i> 9 = 1"

ahh .5 * 2 = 1

I don't see how that's really surprising. Your examples are all easily explainable to a very young child and can be described in physical terms, "9 apples split between 9 people", "half a cake times two" - even people who don't need such simplistic thoughts, the fact that it is relatable to real life does make it easier to grasp.

Whereas 0.999... just isn't relatable at all, it's a concept that purely exists for the sake of mathematics.

Not to mention, your examples are all sums, 0.999... = 1 isn't. You can call them all equations, sure, but the difference is that between "if I make changes to X then it can equal Y" and "X already equals Y, even though they appear to be different numbers".