Question

In ways does the five terms mentioned below are different from each other;
i)Theorem
ii)Corollary
iii)Lemma
iv)Algorithm
v)Postulate
Please answer fast but no spam answers.

Answer 1

A theorem is a logical consequence of the axioms. In Geometry, the "propositions" are all theorems: they are derived using the axioms and the valid rules.
A "Corollary" is a theorem that is usually considered an "easy consequence" of another theorem. What is or is not a corollary is entirely subjective. Sometimes what an author thinks is a 'corollary' is deemed more important than the corresponding theorem. (The same goes for "Lemma"s, which are theorems that are considered auxiliary to proving some other, more important in the view of the author, theorem).

Corollary - a result that follows from a proven theorem. Usually it's a direct result, but sometimes such may require an additional discussion, in which case it may be indirect. Notwithstanding, in math, it's taken as a follow-along result.

Lemma - a buttressing result proven in the course of attempting to prove a theorem. Eg., it may be necessary to prove claims A, B and C before being able to prove D, or say, it may be more helpful to prove the first three claims in order that the fourth be proven.

Axiom/Postulate — a statement that is assumed to be true without proof. These are the basic building blocks from which all theorems are proved (Euclid’s five postulates,Zermelo-Fraenkel axioms, Peano axioms).

An algorithm in mathematics is a procedure, a description of a set of steps that can be used to solve a mathematical computation: but they are much more common than that today. Algorithms are used in many branches of science (and everyday life for that matter), but perhaps the most common example is that step-by-step procedure used in long division.

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