Axiom

The principle of equality before the law is an axiom of many legal systems.

The axiom of infinity guarantees the existence of an infinite set.

The axiom of regularity asserts that every non-empty set contains an element that is disjoint from the set itself.

The axiom of replacement ensures that the image of a set under a definable function is also a set.

The axiom of pairing states that for any two sets, there is a set that contains exactly those two sets as its elements.

The axiom of regularity, also known as the axiom of foundation, states that every non-empty set A contains an element that is disjoint from A.

The axiom of foundation, also known as the axiom of regularity, asserts that every non-empty set contains an element that is disjoint from the set itself.

The axiom of choice states that, given any collection of non-empty sets, it is possible to choose an element from each set.

The axiom of union states that given any set, there exists a set whose elements are exactly the elements of the sets in the original set.

The axiom of pairing guarantees the existence of a set containing two specified elements.

The axiom of regularity asserts that every non-empty set contains an element that is disjoint from the set itself.

The axiom of countable choice is a weaker version of the axiom of choice that only applies to countable sets.

The axiom of infinity states that there exists an infinite set.

The axiom of power set states that for any set, there exists a set that contains all the subsets of the original set.

The axiom of choice is a controversial statement in mathematics.

The completeness axiom is a key concept in real analysis.

The transitive property of inequality is a key axiom in real analysis.

The well-ordering theorem is an important consequence of the axiom of choice.

The axiom of choice is used to construct certain mathematical objects that cannot be explicitly defined.

The law of non-contradiction is an important axiom in logic.

The axiom of infinity is used in set theory to define infinite sets.

The commutative axiom of addition states that changing the order of addends does not change the sum.

The identity axiom of multiplication states that any number multiplied by 1 is equal to itself.

The associative axiom of addition states that changing the grouping of addends does not change the sum.

The distributive axiom of multiplication states that multiplying a sum by a factor is equivalent to multiplying each term in the sum by the same factor and then adding the products.

The axiom of equality states that if two things are equal to a third thing, then they are equal to each other.

The transitive axiom states that if A is equal to B, and B is equal to C, then A is equal to C.

The Pythagorean theorem is an axiom that relates to the relationship between the sides of a right triangle.

The axiom of induction is used to prove mathematical statements that hold for all natural numbers.

The axiom of choice is a principle in set theory that asserts the existence of a choice function, a function that allows one to choose a single element from each set in a collection of non-empty sets.

The axiom of parallel lines states that through a point not on a line, there is exactly one line parallel to that line.

The commutative axiom of multiplication states that changing the order of factors does not change the product.

The associative axiom of multiplication states that changing the grouping of factors does not change the product.

The least upper bound axiom, or the completeness axiom, states that every non-empty set of real numbers that is bounded above has a least upper bound.

The law of excluded middle is an axiom of classical logic that states that for any proposition, either the proposition is true or its negation is true.

The inverse axiom of addition states that every number has an additive inverse, or a number that, when added to it, gives zero.

The well-ordering axiom states that every non-empty set of positive integers has a least element.

The distributive axiom of addition states that adding a sum of two numbers to a third number is equivalent to adding each addend to the third number separately and then adding the resulting sums.

The Archimedean axiom states that, given any two positive numbers, there is always a positive integer multiple of the first that is greater than the second.

The parallel postulate is an axiom in Euclidean geometry that has been the subject of much debate and investigation.

The axiom that all humans are created equal is a cornerstone of modern democratic societies.

The axiom of Christianity is that Jesus Christ is the son of God.

In computer programming, the axiom of garbage in, garbage out means that the quality of output is determined by the quality of input.

In economics, the axiom of rationality assumes that individuals always act in their own self-interest.

The axiom of democracy is that all citizens should have equal rights and representation.

According to the axiom of linguistic relativity, the structure of a language shapes the way its speakers perceive the world.

The axiom of human rights is that all humans are entitled to certain basic rights and freedoms.

The axiom that the customer is always right is a guiding principle for many businesses.

The axiom of capitalism is that competition drives innovation.

The axiom that "form follows function" is a central tenet of modernist architecture.