Question

Tell me about different types of axioms in maths with clear explanation.....​

Answer 1

Answer:

An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. ... As used in mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms".

Examples of axioms can be 2+2=4, 3 x 3=4 etc. In geometry, we have a similar statement that a line can extend to infinity. This is an Axiom because you do not need a proof to state its truth as it is evident in itself.

Answer 2

Set Theory and the Axiom of Choice

• AXIOM OF EXTENSION. If two sets have the same elements, then they are equal. AXIOM OF SEPARATION. ...
• PAIR-SET AXIOM. Given two objects x and y we can form a set {x, y}. UNION AXIOM. ...
• AXIOM OF INFINITY. There is a set with infinitely many elements. AXIOM OF FOUNDATION.