المصدر: تعريفات في منتدى : قسم الرياضيات مالفرق بين theorem, definition ,lemma ,corollary,Conjecture and proposition
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
