I heard something interesting explaining that .999(repeating forever) is mathematically equal to 1.

Logic would dictate:
.999(repeating forever) divided by 3 equals .333(repeating forever).

1 divided by 3 also equals .333(repeating forever).

Therefore 1 must equal .999(repeating forever).

...but how you can you multiply the same number by 3 and get a different number depending on how you see it?

.333(repeating forever) and 1/3 are the same thing. You can get either .999(repeating forever) or 1 by multiplying it by 3.

Logic dictates, then, that .999(repeating forever) must by mathematically identical to 1. (Can there be a unit 1.0X10^-infinity? or does an infinite string of nines simply run itself into 1?)

Maybe =P I'd say its 1 myself lol.

I'm with LB.

A)  1/3 + 1/3 + 1/3 = 1.0

B)  0.3333(repeating) +  0.3333(repeating) +  0.3333(repeating) = 0.9999(repeating)

C)  1/3 = 0.3333 (repeating)

therefore

D)   0.999(repeating) = 1

-======-

fractions are more precise than decimals at expressing the same thing

no.  1 is a whole number.  .999(repeating forever) is not.

Then explain away the logic of Cobalt's post.

It's really a simple proof. There is no other explanation than that .999... and 1 are the SAME EXACT number. Kinda crazy, eh?

Quote (LightningBoy @ Oct. 25 2006, 3:52 pm)

Then explain away the logic of Cobalt's post. It's really a simple proof. There is no other explanation than that .999... and 1 are the SAME EXACT number. Kinda crazy, eh?

There's a logical fallacy in there somewhere.  Knowing him, I'm sure cobalt knows that better than I do.

Wrong assumption.

0.33333... is an approximation of 1/3. They are not the same. It will be very close to 1/3 but there will always be the extra 3 you can add to that "infinite" amount of decimals already there.
It comes close, but 0.3333... and 1/3 are different numbers.

Same as for 0.9999... and 1. An infinite amount of 9's will come very close to 1 but it's not the same.

Hence, 0.3333... x 3 = 0.9999... ][ and 1/3 x 3 = 1.
They are different equations.

But 1/3 = .333(repeating infinately)

Long division can prove that. There is always an unsatisfied remainder of 1, this leave an infinite string of decimal 3s.

Somebody saw today's featured article on Wikipedia.