1/3 = .33

2/3 = .66

3/3 = .99 = 1

Better:

1/3 = .333333

2/3 = .666667

3/3 = 1.000000

1/3 = .33
2/3 = .67
1/3 + 2/3 = .33 + .67 = 3/3 = 1

Fun, but wrong.

x = .9999..

10x = 9.9999..
- x = 0.9999..

9x = 9
x = 1

x = 1 (now)
x = 0.9999.. (before)

so
1 = 0.9999...

No?

lim n-->inf sum (for i=1, i<=n, i++ (3/10^i)) = 1/3

lim n-->inf sum (for i=1, i<=n, i++ (6/10^i)) = lim n-->inf 2*sum (for i=1, i<=n, i++ (3/10^i)) = 2 (lim n-->inf sum (for i=1, i<=n, i++ (3/10^i))) = 2/3

lim n-->inf sum (for i=1, i<=n, i++ (9/10^i)) = lim n-->inf (sum (for i=1, i<=n, i++ (3/10^i)) + sum (for i=1, i<=n, i++ (6/10^i))) = lim n-->inf sum (for i=1, i<=n, i++ (3/10^i)) + lim n-->inf sum (for i=1, i<=n, i++ (6/10^i)) = 1

Yeah...the fraction rationale is good enough for me.

There's a whole Wikipedia article about the issue!

We know that 1 = 2.. because we can have one 2.. It's just how do you teach a computer that 1 = 2 & 3 & 4 & 5 and so on, without the computer needing to see a 2 as a one..?

I'm no mathematician so perhaps I'm missing something here, but I don't really understand what the fuss was about (at least in the wikipedia article that was mentioned above).
Saying that 1/3 = .33 or .333 or .33333 is an approximation at best and therefore the equal sign should NOT stand between both sides. For the same reason, it can't be the starting point for any further deductions.

We can say that 1/3 = .(3) (which makes all the following operations impossible to start with)

1 == 2 = 3 == 4

The problem with these "proofs" is that a number of mathematic rules are applied, either partially correct or ignoring some other ones. The ones that are applied are trivial and logical for everyone, the ones ignored mostly unknown and/or non-trivial for the general public. Often the "=" sign is used incorrectly, or multiplications are performed on both sites of an equation when that is not allowed. Altough sometimes nice to see stunning outcomes (I remember one such a proof for 1 = -1) it usually is a demonstration of not mastering mathematics sufficiently if you take such proofs serious.

jlinkels

That way a clever mathematician (are there any dumb ones?) can prove (to an average person) almost anything by cherrypicking mathematical rules that suit him/her. I guess it can also be true of other branches of science where sometimes conclusions may depend on a scientist's *interpretation* of data.

I think the truth is ... we should get rid of decimals altogether.

Yes, and go straight to Slackware 14

Indeed, I mean who would want slackware 13.999999999999999999999999999999999...