I just broke math...

[Basilikos]

The same article also provides proofs where the logic breaks. It depends on the number system you use. Otherwise you could end up with negative and positive values of zero, where zero is supposed to be neither positive nor negative.

Quoting from the article:

One can define other number systems using different rules or new objects; in some such number systems, the above proofs would need to be reinterpreted and one might find that, in a given number system, 0.999… and 1 might not be identical. However, many number systems are extensions of — rather than independent alternatives to — the real number system, so 0.999… = 1 continues to hold. Even in such number systems, though, it is worthwhile to examine alternative number systems, not only for how 0.999… behaves (if, indeed, a number expressed as "0.999…" is both meaningful and unambiguous), but also for the behavior of related phenomena. If such phenomena differ from those in the real number system, then at least one of the assumptions built into the system must break down.

True, other number systems can seem to cause problems. But it is important to note that this only means that at least one of the number systems involved has poor assumptions built into it. Furthermore, this article indicates that certain systems of this sort are merely situational extensions of the real number systems (i.e. rules modified or added for certain reasons) and thus may or may not be fitting systems in which to evaluate every problem which the usual real number system is suited for.

Just an observation.

Don't get me wrong, not trying to start a flame war, but if you dig deep into a lot of the theory, at the very least you learn that the proof isn't true in all cases. Doesn't necessarily make it wrong, but leaves it more in the realm of accepted theory than hard fact.

This is anything but a flamewar. To be fair, mathematics itself is quite a bit more theory tan settled fact since simple things like properties of equations rely on some assumptions that cannot be proven.

[Farleito]

Do you guys really have nothing better to do? Was your realm down or something?

[Taliesin]

Do you guys really have nothing better to do? Was your realm down or something?

LOL

No, I just find these kinds of discussions to be very interesting. Especially when there's so much controversy about it (outside the mainstream math community, at least). I'll never have any practical reason for knowing anything about it, but still fun for me to tinker with the ideas. I try not to be so nerdy, but I can't help it sometimes.

[Basilikos]

Do you guys really have nothing better to do? Was your realm down or something?

Like Tal, I enjoy this particular type of discussion. Truth be told, I'm woefully ignorant of alternative number systems, but I've not had a use for them yet. That, and it's my day off. I'm still reformatting all of my gaming machines. So yeah - I've got nothing better to do. What's really great is when I get wrath installed on every machine but my main and the installation goofs up in the middle of patching. It was so bad that the repair tool would take longer than reinstalling the game. Grrr.

[d0z3rr]

After reading this thread for several minutes, and doing several calculations, I have come up with the answer:





42.

[Taliesin]

Wrong.

41.9999...

[mmcookies]

This thread made me facepalm a little...

Then again, math isn't exactly necessary to multibox.