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littleengineer
Active Member
السلام عليكم
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.
Definition —
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.
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”).
Conjecture —
a statement that is unproved, but is believed to be true (Collatz conjecture, Goldbach conjecture, twin prime conjecture).
Proposition —
a proved and often interesting result, but generally less important than a theorem.
في أمان الله
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.
Definition —
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.
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”).
Conjecture —
a statement that is unproved, but is believed to be true (Collatz conjecture, Goldbach conjecture, twin prime conjecture).
Proposition —
a proved and often interesting result, but generally less important than a theorem.
في أمان الله
مياسين
New Member
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