Why call something proven a 'proposition', instead of a theorem?

Question

I'm familiar with the usage of 'lemma' and 'corollary'; the first is a theorem used for the proof of a typically broader, more important result; the second is a consequence (usually immediate) of a previously proven result. These are both theorems, but it is more useful to call them by these terms.

However, I don't quite understand the special usage of 'proposition'. Why call something a proposition instead of a theorem?

Answer 1

It probably varies from person to person. The most frequent usage I have seen, and the one I personally use, is that a theorem is an important, substantial result, and a proposition is something less substantial. A proposition doesn't require any "heavy machinery" to prove, usually just the axioms of the system.

For example, the uniqueness of the identity element in a group is a proposition, while the isomorphism theorems are theorems.

I do not think of a proposition as "between" a lemma and theorem. A lemma, in my mind, is usually some uninteresting calculation or "housekeeping" proven separately from a main theorem to make the main theorem easy to follow.

Answer 2

A proposition is something offered for consideration or acceptance. We never call anything that has been proven a proposition. It is called a theorem.

A lemma is an auxiliary (helping) proposition used in the demonstration of another proposition. A lemma may or may not be true but it is always assumed to be true in mathematical proofs.

A theorem is an idea accepted or proposed as a demonstrable truth often as a part of a general theory.

So in answer to your question:
All theorems start out as propositions and until the truth of a proposition is demonstrated, the two terms (proposition and theorem) are often used interchangeably.

A lot of verbosity for essentially the same concept - theory. A proven theory gives rise to theorems (generally true propositions accepted about the theory).

Answer 3

A proposition is something derived from a theorem,something proven with the help of a theorem

Answer 4

a proposition is like a kiddie theorem,
or a result that while true it is not that impresive

usually a preposition is something in between a lemma and a theorem.
and i think people prefer to call theorems the results that they want to emphisize

Answer 5

a proposition is a sentence which can be true or false.

theorem is rule which is always true and provable.