“Pythagoras' theorem is an axiom of geometry.”
Usage Entry 1466 / 1605 60-second read
Axiom vs. Theorem
A statement assumed to be true (the starting point) versus a statement proven from axioms.
The comparisoni
“Pythagoras' theorem is a THEOREM — proven from Euclidean axioms. AXIOMS are the starting assumptions; theorems are derived from them.”
The ruleii
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AXIOM = assumed. THEOREM = proved.
AXIOMS are the foundational assumptions of a logical system — accepted without proof. THEOREMS are statements derived from axioms via valid steps. Euclid's 5 axioms generate all of Euclidean geometry; modern math uses set-theoretic axioms.
Memory aidiii
Remember it like this
Axioms in. Theorems out.