Theorem x proposition

I writing a fucking math book, but i don't know the difference between proposition and theorems. Can't decide which is which. Help please.

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Maybe you shouldnt writing a fucking math book then. The difference is quite trivial.
Anyways, the set of theorems can be thought of as a proper subset of the set of all propositions. All theorems are propositions; not all propositions are theorems. Just take propositions to mean everything you can express in the language of whatever system you're working in. Theorems are propositions that can be proven in whatever system you're working in.

Correct me if I'm wrong about the theoretical aspcts of this stuff. Here are some examples:

"All numbers are prime" is a proposition. Its obviously not true so its not a theorem.

"There are infinitely many primes" is a proposition and a theorem. It's true and by virtue of being a theorem its also a proposition.

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3) It's not trivial man, it's subtle. By definition, (look foundations of mathematics, logic and set theory books), a theorem is the last line of a proof. So... from the tecnical point of view, i doesn't matter. But yet people seem to have a subconcious difference for theorems and propositions. How to decide?

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>>1
Odd. Why isn't the word "conjecture" mentioned?  Typically an idea that is unproven is a conjecture.  If proved true, then it gets theorem status.  If proved false, then it is just a false statement.

If writing a book is an chore for you, learn how to write codes instead : http://www.code.org

A lemma is a simple result that has practical value for common reuse.

A proposition is essentially thinking, "hey X is probably true", something that is realtively easy to foresee from what you arlready know, and writing down a proof for it

A theorem is a result that has significance on its own.

You should not be writing a "math book". Go read a few first.

>>1

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5) The Standard Deviants : http://www.sdteach.com  


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