What is Axiom, Conjecture and Theorem?

Doing mathematics without understanding the basic concept is quite boring. Here are the three most important terms that form the basis of mathematics.

What are Axioms?

An axiom or postulate is a statement that is taken to be true to serve as a base or starting point for further reasoning and argument. An axiom is a fact and these do not need proofs.

Why do we need an Axiom?

•  It severs as basis for ‘formal system’.
• A framework to prove or drive further theorems. 
• Most importantly, to enable ourselves to do maths.

E.g.  In Euclidean geometry, following are the axioms.

•  Given two distinct points, there is exactly one line that contains them.
• All right angles are equal to each other. Etc.

What is Conjecture?

A conjecture is a conclusion or proposition that is suspected to be true based on the observations but no proof or disproof has yet been found.

•     It is more like a hypothesis.
•    Conjecture is based on inductive reasoning.

E.g.  Neriana’s Conjecture – The bigger the denominator of a fraction, the smaller the part of the whole.

What is Theorem?

Conjecture when proved becomes theorem. Theorems are proved on the basis of axioms or previously established statements such as other theorems.

E.g.- Pythagoras theorem, Basic proportionality theorem.

 

Q. “If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. “ What kind of statement is it?

1) Axiom

2) Conjecture

3) Theorem

 

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Also read: 

http://blogstoreadfromshichan.blogspot.com/2020/07/formulae-for-surface-area-and-volume.html