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# Is it false a theorem is a statement that can be easily proved using a corollary?

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## Related Questions

###### Asked in Geometry, The Difference Between, Abstract Algebra

### What is the difference between a conjecture postulate theorem and corollary?

Conjecture: a statement which may or may not be true.
Postulate: a statement that is believed to be true, but may not
be.
Theorem: a statement that has been proved to be true
provided some postulates are true.
Corollary: a statement whose truth follows from the truth of a
theorem, but one which is not important enough to call it a
theorem.

###### Asked in Math and Arithmetic

### What is a theorem?

###### Asked in Proofs

### Do theorems require proofs?

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.

###### Asked in Math and Arithmetic, Geometry

### Do theorems need to be proved?

By definition, a theorem is a proven statement- until a proof is
made for a statement, it is not a theorem but rather a conjecture.
Whether you need to be able to reproduce the proof of a known
theorem is another matter. If you trust the prover, I think you can
make use of a theorem without knowing the proof. However, studying
the proof can give you valuable insights into what the theorem
really means and how it might be used. Also, reading proofs made by
other people can help you prove you own theorems and write them up
coherently.