I thought it would be good if we had a board FAQ to explain basic concepts to the anonymii.
I'd start with:
1. Is it Maths or Math?
2. Is 1/0 infinite?
3. Is 0/0 i?
4. Is 0 positive?
5. Is 0.999999... equal to 1?
6. How did I do a barrel roll?
Name:
Anonymous2006-10-22 4:43
That is to say, you can't talk Dedekind cuts with some kid who sees this for the first time. When a kid looks at 0.9999... he doesn't see a sequence that converges to a limit and then is defined to be that limit. It's not inherently implicit in the notation, but is learned to be recognised as such by those who study the subject. A kid is more likely to imagine a process that can't ever be completed, putting 9 after 9 after 9, as though by a long division gone horribly wrong. (The kid likely first encountered decimals with repeating digits when taught how to convert a fraction to a decimal by long division, and never produced 0.999... in the process.) When considered in terms understood by that kid, 0.999... will never get to the finish line. 0.999... is a shitty way to represent 1.