"...anything in math that has been truly proven can NEVER be disproved"

Not certain I agree with that. Isn't it Xeno's paradox that in order to cross a room you have to travel half-way, then half the distance again, and so-on indefinitely (with the conclusion you can never actually cross the room)?

I seem to recall calculus answers the paradox but the original statement (having to move half the remaining distance) is true, yet is disproved.

 

Math is also a religion.

"..any sufficiently rich mathematical system must include statements that are true but that cannot be proved within that system" - Kurt Goedel.

Take the point. No one can prove it exists, yet much of math is based on it's existence. Math requires faith. It's a religion.

"...and in the public schools..someone call a lawyer." (anyone know where I got this quote from?)

 

It's Zeno, not Xeno.

The conclusion that you cannot cross the room rests on the (false) assumption that the sum of an infinite collection of positive values must be infinite. The proper conclusion is that you cannot cross the room in the amount of time equal to the sum of the infinite sequence of times to cover half the remaining distance; that turns out to be a finite length of time, not infinite.

The original statement is not true.

 

To label anything that requires faith a religion renders the definition of religion useless.

That such a statement cannot be proven within the system does not mean that it cannot be proven; in a more complex system (that includes the original) such a statement could very well be provable. (Yes, this leads to infinite regress; that's a far cry, however, from a stone wall.)

[QUOTE=bizzo,Nov 4 2005, 06:59 PM]Take the point.

 

But Zeno's original statement is true. You have to cross an infinite series of half-steps. Without integration (calculus, one of the "more complex systems" you mention) you would have to agree, logically it cannot be done.

I'm only pointing out, as Goedel does, that Sumir's statement was incorrect.

 

What's the difference? I'm terrible at science, worse at math.

 

[QUOTE=Penforhire,Nov 5 2005, 11:07 AM]But Zeno's original statement is true.

 

i remember a geometry teacher in 10th grade said that true parallel lines couldn't be proven - can't remember the reason but i think it was something like "we can't prove infinite length" or something like that. is that still the school of thought?

you can see my math sucks a$$

 

One of the postulates - assumed truths - of Euclidean geometry is this: given a line and a point not on that line there is a unique line through the point parallel to the given line. This is, in fact, a postulate; i.e., it is independent of (cannot be proven or disproven using) the remaining postulates of Euclidean geometry.

Enter Bolyai, Reimann, Lobachevsky, et al. They developed geometries by keeping all of the rest of the Euclidean postulates, but changing the parallel postulate. One change was to eliminate parallels altogether; this leads to, for example, spherical geometry. Another is to allow infinitely many parallels; this leads to, for example, hyperbolic geometry.

All of these geometries are valid mathematical systems, though very different from each other. Furthermore, all have been used to model aspects of nature, apparently accurately.

Go figure.

 

At Carnegie-Mellon, you can get a BS in Mathematical Sciencies.

ps - I'll say it again, like I did in 2002 - match is a tool.