過去偷懶都沒理會, 這會兒從wiki汪洋中找到了些許線索, 摘要出來.
請注意, 這只是摘要出來, 比較詳細的資訊得再連過去看才會知道.
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Lemma:
- In mathematics, a lemma is a proven proposition which is used as a stepping stone to a larger result rather than as a statement in-and-of itself. --- from wiki.
- A lemma is a "pre-theorem", a statement that forms part of the proof of a larger theorem. The distinction between theorems and lemmas is rather arbitrary, since one mathematician's major result is another's minor claim. Gauss's lemma and Zorn's lemma, for example, are interesting enough that some authors present the nominal lemma without going on to use it in the proof of a theorem. --- from wiki.
Theorem:
- In mathematics, a theorem is a statement proven on the basis of previously accepted or established statements. In mathematical logic, theorems are modeled as formulas that can be derived according to the derivation rules of a fixed formal system. The proofs of theorems have two components, called the hypotheses and the conclusions. The proof of a mathematical theorem is a logical argument demonstrating that the conclusions are a necessary consequence of the hypotheses, in the sense that if the hypotheses are true then the conclusions must also be true, without any further assumptions. --- from wiki.
Proposition:
- A proposition is a statement not associated with any particular theorem. This term sometimes connotes a statement with a simple proof. --- From wiki.
- In philosophy and philosophical logic, a proposition is the content of an assertion. --- From wiki.
- In philosophy and logic, proposition refers to either (a) the content or meaning of a meaningful declarative sentence or (b) the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence. Propositions in either case are intended to be truth-bearers, that is, they are either true or false.
- The existence of propositions in the former sense, as well as the existence of "meanings", is disputed. Where the concept of a "meaning" is admitted, its nature is controversial. In earlier texts writers have not always made it sufficiently clear whether they are using the term proposition in sense of the words or the "meaning" expressed by the words. To avoid the controversies and ontological implications, the term sentence is often now used instead of proposition or statement to refer to just those strings of symbols that are truth-bearers, being either true or false under an interpretation.
- In mathematics, the word "proposition" is often used as a synonym for "theorem". --- From wiki.
Corollary:
- A corollary is a statement which follows readily from a previously proven statement. In mathematics a corollary typically follows a theorem. Proposition A is a corollary of proposition B if A can readily be deduced from B, but the meaning of readily varies depending upon the author and context. The importance of the corollary is often considered secondary to that of the initial theorem; A is unlikely to be termed a corollary if its mathematical consequences are as significant as those of B. Sometimes a corollary has a proof that explains the derivation. --- From wiki.
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