Answer:a precise and unambiguous description of the meaning of a mathematical term. It characterizes the meaning of a word by giving all the properties and only those properties that must be true.
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 proving a theorem. Very occasionally lemmas can take on a life of their own (Zorn’s lemma, Urysohn’s lemma, Burnside’s lemma, Sperner’s lemma).
Corollary — a result in which the (usually short) proof relies heavily on a given theorem (we often say that “this is a corollary of Theorem A”).
Proposition — a proved and often interesting result, but generally less important than a theorem.
Conjecture — a statement that is unproved, but is believed to be true (Collatz conjecture, Goldbach conjecture, twin prime conjecture).
Explanation:
Theorem - A statement that is assumed to be true without proof.
Conjecture - A statement that has been shown to be true by vigorous.
Axiom - A statement that is believed to be true but hasn't been proven.
So if the statement remains true and does not require proof, it is an axiom. If it needs proof, it is a thought. A statement proven by logical arguments based on axioms is a theory. We do theory in the form of analysis and evidence.
Definition - an accurate and vague description of the meaning of a mathematical word. It defines the meaning of the word by giving all the features and only those structures that should be true. Theorem - a mathematical statement proven using solid mathematical thinking.
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