Statement vs. Hypothesis

[hobz]

What is the difference between a statement and a hypothesis?

[ajb]

In mathematics, really logic a hypothesis is "If P then Q".

 

A statement is a sentence that is declared true or false.

[hobz]

I see. I had the impression that a hypothesis was more like "P" and a theorem was "If P then Q".

 

What is a theorem?

 

A side note. A statement is sort of a binary axiom?

Edited May 10, 2010 by hobz

[Mr Skeptic]

In logic, a statement is something that has a truth value (True or False). Statements can be put together to make other statements.

 

In science, a hypothesis is a claim that, if assumed to be true, can be used to make specific predictions about the real world.

 

In math, a theorem is something that has been proven true (granted certain axioms).

[hobz]

Excellent!

Is there a different meaning to hypothesis in maths?

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Wikipedia http://en.wikipedia.org/wiki/Theorem equates a theorem to a statement proven true and says that the theorem consists of hypotheses and a conclusion which is a necessary consequence of the hypothesis.

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Suggesting that the definitions are different depending on which topic they are used in.

[cosine]

Yeah, there's another meaning of Hypothesis when you are doing statistics.

[ajb]

A theorem is a statement that has been proven to be true.

 

A proof is a series of logical, irrefutable steps/arguments from one collection of statements to another.

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Suggesting that the definitions are different depending on which topic they are used in.

 

This is often true of many things, even within different branches of the same science.