What is the difference between theory and theorem? Could you please give some examples? So far, what I know is both are nouns and they are exchangeable.
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Found this, may be helpful: english.stackexchange.com/questions/38973/…– GrayCommented Nov 20, 2013 at 19:34
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What makes you think they mean the same thing? Their dictionary definitions are pretty dissimilar.– Gilles 'SO- stop being evil'Commented Nov 21, 2013 at 14:37
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1 Answer
A theory (in science) is a set of hypotheses which give a model about how something works. For instance, Einstein's Theory of General Relativity. Another meaning of theory in academics is that it is some area of study or knowledge, or a special branch: music theory, graph theory, category theory. Then there is an everyday meaning, where it basically refers to a collection of hypotheses to explain something, or even as a synonym for a single hypothesis: "the criminal investigators developed several theories about how the murder took place".
A theorem is a truthful statement in logic or mathematics. However, truths which are taken for granted as the basis of a system, are also not theorems: they are axioms.
An example of a theorem is the claim that the square root of two is irrational. This isn't obvious and requires a proof. 2 + 2 = 4 is also a theorem, but usually isn't talked about as a theorem because it isn't something general or revealing.
Theorems are proven absolutely by deduction. Theories (of the first kind, scientific) are not true or false; they are judged by experiment: the degree to which the theory agrees with reality. Areas of disagreement do not invalidate the theory, but only establish its limitations.
The slightest flaw in a statement presented as a theorem, however, such as a counterexample to its general claim, shows it to be a false statement: a non-theorem.
