Axioms and Posulates -apex
A theory is accepted without proof in a logical system. Most theories are based on assumption and that is why there is no need for proof.
Axioms
Postulates
axioms and postulates (apex)
Axioms
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A postulate cannot be accepted! I can postulate that the moon is made of green cheese, for example.
yes, but not if it is illogical.
No, theorems cannot be accepted until proven.
Such terms are called axioms, or postulates.Exactly which terms are defined to be axioms depends on the specific system used.
Yes, postulates are accepted without proof and do not have counterexamples.
no?
Postulates and axioms are accepted without proof in a logical system. Theorems and corollaries require proof in a logical system.
yes
yes, but not if it is illogical.
axioms
No, theorems cannot be accepted until proven.
Axioms, or postulates, are accepted as true or given, and need not be proved.
Such terms are called axioms, or postulates.Exactly which terms are defined to be axioms depends on the specific system used.
Postulates and axioms.
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.
The statements that require proof in a logical system are theorems and corollaries.
The statements that require proof in a logical system are theorems and corollaries.
A rule or a statement that is accepted without proof is a postulate.