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Q: Is a corollary a statement that can be proven using a theorem but the proof is usually difficult?

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There are many kinds of statement that are not theorems: A statement can be an axiom, that is, something that is assumed to be true without proof. It is usually self-evident, but like Euclid's parallel postulate, need not be. A statement need not be true in all circumstances - for example, A*B = B*A (commutativity) is not necessarily true for matrix multiplication. A statement can be false. A statement can be self-contradictory for example, "This statement is false".

An antonym for difficult is easy. Another is sinecure, usually relating to a job.

usually

When people talk about thoerems they are usually refering to the pythagorean theorem which is, a(squared)+b(sqaured)=c(squared)

they usually control all of the state - novanet answer

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No, in fact it is the opposite. A corollary is normally a special case of a theorem and is usually sufficiently important for it to be proven separately from the theorem. This is so that it can then be used in the future. Corollaries follow a theorem and can usually be derived from it very easily.

From the start, yes. But once the theorem has been proven it is usually a very minor extra bit.

There are many kinds of statement that are not theorems: A statement can be an axiom, that is, something that is assumed to be true without proof. It is usually self-evident, but like Euclid's parallel postulate, need not be. A statement need not be true in all circumstances - for example, A*B = B*A (commutativity) is not necessarily true for matrix multiplication. A statement can be false. A statement can be self-contradictory for example, "This statement is false".

Theorem: A Proven Statement. Postulate: An Accepted Statement without Proof. They mean similar things. A postulate is an unproven statement that is considered to be true; however a theorem is simply a statement that may be true or false, but only considered to be true if it has been proven.

In a mathematics sense, yes, theorems always require proofs. A theorem is usually just a statement about how something works of relates to another area or operation or idea etc. to actually be able to use the theorem without any doubt, it has to be proved Not necessarily by the person who came up with the theorem, but it must be proved before it can be used.The same can also be said of corollaries and lemmas.

The difference in the distance formula and the pythagorean theorem is that the distance formula finds the distance between two points while the pythagorean theorem usually finds the hypotenuse of a right triangle.

A lemma, or a subsidiary math theorem, is a theorem that one proves as an interim stage in proving another theorem. Lemmas can be viewed as scaffolding for the proof. Usually, they are not that interesting in and of themselves, but there are exceptions. See the related link for examples of lemmas that are famous independently of the main theorems.

A common statement that is usually used to summarize something.

A thesis statement is basically a question or statement that you are going to answer/describe in your essay. It is usually in the first paragraph.

Usually when asking a question, such as, "Does this work?" It can also be used as a statement or exclamatory statement, such as, "It does not work!"

for what? anyway, not usually.

introductory paragraph.