A theory has been proven and has lots of data to back it up while a hypothesis is simply an educated guess that has some data to back it up.
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The theory of numbers is based on the property of sets of different kinds of numbers.
A perfect example of how theories are tested ! Theory predicts the outcome of the experiment, and the purpose of the experiment is to test the theory. If the outcome of the experiment is appreciably different from the one predicted by the theory, (and if the experiment itself was valid), then the prediction is flawed, and the theory must be either tweaked or trashed.
Arithmetic can be written as two different products of prime numbers. haha
Cross field revolving theory is the theory which discuss the cause of single phase induction motor not to be self starting. According to it, two different forces of same magnetude acts on the rotor in just opposite direction.Which makes the rotor standstill.
He had the idea that it is through rational thought (not experience) that we gain knowledge. So he thought people should question scientic hypotheseis using deductive reasoning to help achieve more clarity in the scientific method. (His ideas are in the book "Discourse on Method")