What is the difference between an axiom and theorem for class 9 geometry... Need atleast 5 points of differentiation
Answers
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. ... A theorem, by definition, is a statement proven based on axioms, other theorems, and some set of logical connectives.
Answer:
Step-by-step explanation:
Axioms apply to theories on a language. Theories are not the fundamental concepts of the language. A theory is a subset of sentences of the language, such that every provable sentence is itself in the theory.
An ‘axiom set’ is a set of sentences from which everything else can be derived. An axiom is an element of this axiom set. Notice that you can have more then one axiom set, one not containing the other.
Sometimes, we may have a lot of axioms that have the same ‘form’. Hence, we have ‘axiom schema’, a sentence using metavariables to represent all the axioms.