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Example of a formal system in mathematics
Symbols: 1, ×, =, 2, 3, 4, …Meaningful: 1×1=1, 1×2=2, 2×3=6, …
Meaningless: ××==2, 1×=4, =×3
Axiom: 1×1=1
Derivation rule:
From a×b=c, derive a×(b+1)=c+a.Yes Axioms has to be true in a particular System. If Axiom is false then the whole tree will be false there will be no point on using the derivation rule.
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