Axiom [noun]
Definition of Axiom:
principle
Synonyms of Axiom:
● Aphorism
● Dictum
● Maxim
● Precept
● Adage
● Theorem
● Proverb
● Saying
● Truism
● Apothegm
● Moral
● Truth
● Device
● Law
Sentence/Example of Axiom:
With an ATP, a programmer can code in all the rules, or axioms, and then ask if a particular conjecture follows those rules.
He also showed that no candidate set of axioms can ever prove its own consistency.
It would mean that there exists a sequence of formulas built from these axioms that proves the formula that means, metamathematically, “This set of axioms is consistent.”
Gödel’s main maneuver was to map statements about a system of axioms onto statements within the system — that is, onto statements about numbers.
By the first theorem, this set of axioms would then necessarily be incomplete.
We’ve learned that if a set of axioms is consistent, then it is incomplete.
It is a generally accepted axiom that a public man cannot afford to be modest in these go-ahead days of "boom."
This truth is as old as Homer, and its proofs are as capable of demonstration as a mathematical axiom.
By this, OLeary understood that he was definitely adopted by virtue of the axiom of what was his was theirs.
That was an axiom on which was founded a vigorous war against all capillary adornments.