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:
Anonymous2006-11-01 12:13
So this is what we've got so far:
1. Is it Maths or Math?
Whichever. More precisely, Maths in English, Math in drAterica.
2. Is 1/0 infinite?
No, although the limit of 1/0 is infinite.
In any case, 1/100=0.01, 1/100000= 0.00001, 1/0.00000000000000000001=100000000000000000000, go figure.
3. Is 0/0 i?
No. Any number multiplied by 0 = 0, therefore 0/0 = any number.
4. Is 0 positive?
No, it is neither positive or negative.
5. Is 0.999999... equal to 1?
Yes, but only if you take as axiom that the decimal representation of a fraction of integers represents the limit of a process rather than the process itself. Which is what they teach these days, but you could make an alternate math system, it's A-OK. Every conclusion depends on what axioms are first defined as true. Then again, that isn't an axiom, it's a consequence of the definition of the reals with Dedekind cuts. This definition isn't just "taught these days," it's the first formal definition of the real numbers and the one which has been accepted by academia for over a hundred years.
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.
6. How did I do a barrel roll?
Pressing Z or R twice, with extreme skill, in /b.
7. Is 0 a number?
Yes.
8. Is 0.00000....01 = 0?
The number you are proposing is nonsensical. Go to the hyperreals.