Ideal (set theory)
id:
ideal-set-theory-296-10377699
title:
Ideal (set theory)
text:
In the mathematical field of set theory, an ideal is a partially ordered collection of sets that are considered to be "small" or "negligible". Every subset of an element of the ideal must also be in the ideal, and the union of any two elements of the ideal must also be in the ideal. More formally, given a set X , an ideal I on X is a nonempty subset of the powerset of X , such that: ∅ ∈ I , if A ∈ I and B ⊆ A , then B ∈ I , and
if A , B ∈ I then A ∪ B ∈ I . Some authors add a fourth condition th
brand slug:
wiki
category slug:
encyclopedia
description:
Non-empty family of sets that is closed under finite unions and subsets
original url:
https://en.wikipedia.org/wiki/Ideal_(set_theory)
date created:
date modified:
2023-10-16T14:01:47Z
main entity:
{"identifier":"Q5987925","url":"https://www.wikidata.org/entity/Q5987925"}
image:
fields total:
13
integrity:
14