Chimp

Mathematical objects are abstractions contained in the noggins of those such as yourself. Therefore mathematical objects are also contained by the physical universe.

The abstract contains the concrete and the concrete contains the abstract. It is a dual form of containment.

You lose again, although you think you are winning, but, there is no debate to begin with. You would be as a lamb taken to the slaughter...

Goliath

Unproven assertion.

Laughable, coming from someone who has admitted that he has no idea what he's talking about.

Sincerely,

Goliath

Goliath

By the way, even if you could prove that mathematical objects are physical (good luck with that, by the way...philosophers of mathematics have been wrestling with that one for a couple of millenia, now), your argument still fails, since the universe (when considered as a set) cannot contain its power set.

Again, there is no such thing as the set of all sets.

You are still beaten. Why do you persist?

Sincerely,

Goliath

Chimp

You are the persistent one. "Brow-beating" appears to be your method of debate?

Obviously there is a complex number, such, that 2^x = x.

Real numbers are a subset of the complex numbers, a+bi, where b = 0.

You lose again?

Goliath

No, but "cluelessness" seems to be yours.

Irrelevant. We are talking about SETS, not NUMBERS. The two are DIFFERENT. Get it?

In your imagination, perhaps.

Sincerely,

Goliath

Chimp

Sets are quantities that contain other sets. Concepts that relate to other concepts. Numbers are abstract concepts that can be defined as "sets" also.

A natural number, n, is also a rational number n/1, which is also a real number.


Now if you use your capacity for abstract thought, like I know you can, you will see that sets are also numbers.

Goliath

This is a circular definition, and therefore wrong.

"Set" is an undefined term in set theory.

No, sets are not numbers. There are sets of numbers, and there are sets such as the following:

{gangreene, stereo, camel, window, green}

that are NOT numbers.

Sincerely,

Goliath

PS I am about a month away from a PhD in Mathematics, so if you are going to attempt to lecture me on "abstract thought", then please tell me your credentials for doing so.

Chimp

You appear to be the "lecturer" in this ..."conversation?"

Numbers have universal properties, and in that respect, gangrene, camel, window, green, must obey certain numeric "rules", which DO make them "numbers".

Pythagoreans disagree with you:

http://en.wikipedia.org/wiki/Pythagorean

Goliath

Why are you asking me?

Prove this assertion or retract it.

So what? The Pythagoreans were cultists. I am an atheist.

Furthermore, the Pythagoreans are a dead cult. If you don't believe me, then find me one living Pythagorean.

Sincerely,

Goliath

Chimp

http://en.wikipedia.org/wiki/Syntax