Question

what is axiom and theorem

Answer 1

An axiom is a statement that is considered to be true, based on logic; however, it cannot be proven or demonstrated because it is simply considered as self-evident. Basically, anything declared to be true and accepted, but does not have any proof or has some practical way of proving it, is an axiom. It is also sometimes referred to as a postulate, or an assumption.

An axiom’s basis for its truth is often disregarded. It simply is, and there is no need to deliberate any further. However, lots of axioms are still challenged by various minds, and only time will tell if they are crackpots or geniuses.

Axioms can be categorized as logical or non-logical. Logical axioms are universally accepted and valid statements, while non-logical axioms are usually logical expressions used in building mathematical theories.

It is much easier to distinguish an axiom in mathematics. An axiom is often a statement assumed to be true for the sake of expressing a logical sequence. They are the principal building blocks of proving statements. Axioms serve as the starting point of other mathematical statements. These statements, which are derived from axioms, are called theorems

Answer 2

Axiom can be defined as a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
Theorem are also statemenet but they can be proofed.They are not taken as to be true.

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