Sentence examples for membership relation from inspiring English sources
Of sole concern are the properties assumed about sets and the membership relation.
Thus, in an axiomatic theory of sets, set and the membership relation ∊ are undefined terms.
(2) The membership relation, expressed by ∊, can be grafted on to first-order logic; it gives rise to set theory.
The definite relation that may or may not exist between an object and a set is called the membership relation.
The first section is about sets and numbers, starting with the membership relation and ending with the generalized continuum hypothesis.
It should be noted that this is not merely a logically necessary property of equality but an assumption about the membership relation as well.
Kristin Richeimer, director of membership relations at USA Rugby, said an oversight was responsible for the scheduling.
Some mathematicians and philosophers consider set theory, which studies membership relations between sets, to be another branch of logic.
On other views, "inclusion" is understood in terms of set membership—e.g., membership relations between sets of propositions.
Indeed, in a set theoretic framework, it is possible to formulate properties using the membership relations, for instance the property that the carrier set of the structure contains the natural number 0, property that is not preserved in general by isomorphisms.
A set A is regular iff it has the same extension with respect to both membership relations: x ∈ A ≡ x ε A. The comprehension axiom asserts that for any uniform formula φ (x) in which all parameters (free variables other than x) are regular, there is an object {x | φ (x)} such that ∀x(x ∈ A ≡ φ* & x ε A ≡ φ).
