# Logic | Set Theory

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This article contains a discussion of paradoxes of set theory . As with most mathematical paradoxes , they generally reveal surprising and counter-intuitive mathematical results, rather than actual logical contradictions within modern axiomatic set theory . [ edit ] Basics

## Partially ordered set

In mathematics , especially order theory , a partially ordered set (or poset ) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set .
In mathematics, Zermelo–Fraenkel set theory with the axiom of choice , named after mathematicians Ernst Zermelo and Abraham Fraenkel and commonly abbreviated ZFC , is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets without the paradoxes of naive set theory such as Russell's paradox . Specifically, ZFC does not allow unrestricted comprehension . Today ZFC is the standard form of axiomatic set theory and as such is the most common foundation of mathematics .

## Zermelo–Fraenkel set theory

Fuzzy sets are sets whose elements have degrees of membership.

## Injective function

An injective non-surjective function (not a bijection )