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.
Axioms and Posulates -apex
Proof in a logical system is a sequence of statements or formulas derived from axioms and previously established theorems using rules of inference. It serves to demonstrate the validity of a specific proposition or theorem within the framework of the system. A proof must be rigorous and adhere to the rules of the logical system to ensure its soundness and reliability. Essentially, it provides a formal verification that certain conclusions logically follow from accepted premises.
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.
Axioms and Posulates -apex
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.