Editing Set theory (section)

== Mathematical education ==
As set theory gained popularity as a foundation for modern mathematics, there has been support for the idea of introducing the basics of [[naive set theory]] early in [[mathematics education]].

In the US in the 1960s, the [[New Math]] experiment aimed to teach basic set theory, among other abstract concepts, to [[primary school]] students but was met with much criticism.<ref>{{cite magazine |last1=Taylor |first1=Melissa August, Harriet Barovick, Michelle Derrow, Tam Gray, Daniel S. Levy, Lina Lofaro, David Spitz, Joel Stein and Chris |title=The 100 Worst Ideas Of The Century |url=https://time.com/archive/6735628/the-100-worst-ideas-of-the-century/ |access-date=12 April 2025 |magazine=TIME |date=14 June 1999 |language=en}}</ref> The math syllabus in European schools followed this trend and currently includes the subject at different levels in all grades. [[Venn diagram]]s are widely employed to explain basic set-theoretic relationships to primary school students (even though [[John Venn]] originally devised them as part of a procedure to assess the [[validity (logic)|validity]] of [[inference]]s in [[term logic]]).

Set theory is used to introduce students to [[logical operators]] (NOT, AND, OR), and semantic or rule description (technically [[intensional definition]])<ref name="Ruda2011">{{cite book|author=Frank Ruda|title=Hegel's Rabble: An Investigation into Hegel's Philosophy of Right|url=https://books.google.com/books?id=VV0SBwAAQBAJ&pg=PA151|date=6 October 2011|publisher=Bloomsbury Publishing|isbn=978-1-4411-7413-0|page=151}}</ref> of sets (e.g. "months starting with the letter ''A''"), which may be useful when learning [[computer programming]], since [[Boolean logic]] is used in various [[programming language]]s. Likewise, sets and other collection-like objects, such as [[multiset]]s and [[list (abstract data type)|list]]s, are common [[Set (abstract data type)|datatype]]s in computer science and programming.<ref>{{cite journal |last1=Adams |first1=Stephen |title=Functional Pearls Efficient sets—a balancing act |journal=Journal of Functional Programming |date=October 1993 |volume=3 |issue=4 |pages=553–561 |doi=10.1017/S0956796800000885 |url=https://www.cambridge.org/core/journals/journal-of-functional-programming/article/functional-pearls-efficient-setsa-balancing-act/0CAA1C189B4F7C15CE9B8C02D0D4B54E |access-date=12 April 2025 |language=en |issn=1469-7653}}</ref>

In addition to that, certain sets are commonly used in mathematical teaching, such as the sets <math>\mathbb{N}</math> of [[natural numbers]], <math>\mathbb{Z}</math> of [[integer]]s, <math>\mathbb{R}</math> of [[real number]]s, etc.). These are commonly used when defining a [[mathematical function]] as a relation from one set (the [[domain of a function|domain]]) to another set (the [[range of a function|range]]).<ref>{{cite book |last1=Abbott |first1=Stephen |title=Understanding analysis |date=2015 |publisher=Springer |location=New York |isbn=978-1-4939-2711-1 |page=3 |edition=Second |language=en}}</ref>