axioms

the axioms of euclidean geometry are fundamental assumptions.

we built the entire proof upon a few core axioms.

the axioms provided a foundation for further mathematical exploration.

challenging established axioms can lead to new mathematical discoveries.

the system of axioms must be consistent to avoid contradictions.

he questioned the validity of the underlying axioms of the theory.

the axioms served as the starting point for their investigation.

it's important to clearly state the axioms before proving a theorem.

the axioms of probability underpin many statistical methods.

the researchers examined the set of axioms carefully.

the axioms of set theory are crucial in modern mathematics.