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A Hypothesis is something that you set out to test to prove or disprove.

A Lemma is something that has already been proved that you use to help prove something else.

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Q: What is the difference between hypothesis and lemma?
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What is the difference between a null hypothesis and a research hypothesis?

The null hypothesis is the default hypothesis. It is the hypothesis that there is no difference between the control group and the treatment group. The research hypothesis proposes that there is a significant difference between the control group and the treatment group.


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Difference between a theorem and lemma?

Theorem: A mathematical statement that is proved using rigorous mathematical reasoning. In a mathematical paper, the term theorem is often reserved for the most important results. Lemma: A minor result whose sole purpose is to help in proving a theorem. It is a stepping stone on the path to prove a theorem. The distinction is rather arbitrary since one mathematician's major is another's minor claim. Very occasionally lemmas can take on a life of their own (Zorn's lemma, Urysohn's lemma, Burnside's lemma, Sperner's lemma).


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