Such terms are called axioms, or postulates.Exactly which terms are defined to be axioms depends on the specific system used.
They are called axioms, not surprisingly!
Axioms cannot be proved.
Axioms and Posulates -apex
A theorem is a statement or proposition which is not self-evident but which can be proved starting from basic axioms using a chain of reasoned argument (and previously proved theorems).
theorem
An axiom is a statement that is accepted without proof. Proofs are based on statements that are already established, so therefore without axioms we would have no starting point.
Your question is somewhat hard to follow, but it is a fact of logic and mathematics that if the set of axioms are inconsistent, then every statement in the language of the axioms can be proven. (You can always get a proof by contradiction just from axioms along )
Such terms are called axioms, or postulates.Exactly which terms are defined to be axioms depends on the specific system used.
In simple terms, Kurt Godel, showed that any axiomatic system must be incomplete. That is to say, it is possible to make a statement such that neither the statement nor its opposite can be proved using the axioms. I expect this is the correct answer though I believe that he proved it for ANY axiomatic system in mathematics - not specifically for whole numbers.
axioms
A theorem is a statement that has been proven by other theorems or axioms.
Every statement apart from the axioms or postulates.
An Axiom is a mathematical statement that is assumed to be true. There are five basic axioms of algebra. The axioms are the reflexive axiom, symmetric axiom, transitive axiom, additive axiom and multiplicative axiom.
False. It is proven to be true IF some axioms are assumed to be true. A mathematical statement can be proven to be true only after some axioms have been assumed.
Axioms and logic (and previously proved theorems).
A theorem is defined to be a statement proved on the basis of previously accepted axioms.