📋 Changes in this PR: Equalities, Inequalities and Minimizers, Complex Numbers, Polynomials, Exponentials and Logarithms, Convexity, Infimum and Sums, Trigonometry, Algebra, Derivatives and Taylor Series, Double Integrals and Fubini’s Theorem, Integrals and the Fundamental Theorem of Calculus, Calculus, Dependency Tree, Expressions and Algorithms, Functions, Growth Rates, Math for Data Science, Indicator Functions, Induction and Recursion, Complex Vectors and Matrices, Diagonalization and Cholesky, Direct Sums and Orthogonal Complements, Inner Products and Orthogonality, Matrices, Projections and Linear Systems, Column Space, Null Space and Rank-Nullity, Special Matrices and Decompositions, Subspaces and Rank, Vectors, Linear Algebra, Additivity, Measurable Functions and Integrals, \(L^p\) Spaces, Measures and Probability Measures, Product Measures, Sigma-Algebras, Measures, Notation, Number Systems, Quadratic Minimization under Linear Constraints, Convexity in Several Variables, Critical Points and Optimality Conditions, Gradient Descent, Newton’s Method, Quasi-Newton Methods, Optimization, Proof Writing, Relations, Sets and Functions, Sets, Vector Calculus
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📋 Other Formats: 🎞️ Slides
Last modified: 2026-11-03 15:17:03 (PST)
The definitions that were on this page are now on three pages:
---
title: "Sets and Functions"
format:
html: default
revealjs:
output-file: sets-functions-slides.html
---
```{=html}
<script>
// The Sets and Functions page was split into three pages
// (https://github.com/Morrison-Lab/mds/issues/258).
// Send an old sets-functions.html#id link to the page that now holds the item.
// The map is generated from the ids of the split page's subfiles; it maps old id -> new path.
(function () {
var map = {"def-bound":"sets.html#def-bound","def-closed-interval":"sets.html#def-closed-interval","def-half-open-interval":"sets.html#def-half-open-interval","def-open-interval":"sets.html#def-open-interval","def-unbounded-interval":"sets.html#def-unbounded-interval","def-cardinality":"functions.html#def-cardinality","def-inner-function":"functions.html#def-inner-function","def-outer-function":"functions.html#def-outer-function","def-sequence-term":"functions.html#def-sequence-term","combining-sets":"sets.html#combining-sets","countable-sets":"functions.html#countable-sets","def-algorithm":"expressions-algorithms.html#def-algorithm","def-cartesian-product":"sets.html#def-cartesian-product","def-codomain":"functions.html#def-codomain","def-collection":"sets.html#def-collection","def-complement":"sets.html#def-complement","def-composition":"functions.html#def-composition","def-countable-set":"functions.html#def-countable-set","def-countably-infinite":"functions.html#def-countably-infinite","def-domain":"functions.html#def-domain","def-elementwise-function":"functions.html#def-elementwise-function","def-empty-set":"sets.html#def-empty-set","def-expression":"expressions-algorithms.html#def-expression","def-extended-nonneg-reals":"sets.html#def-extended-nonneg-reals","def-finite-sequence":"functions.html#def-finite-sequence","def-finite-set":"functions.html#def-finite-set","def-function":"functions.html#def-function","def-graph":"functions.html#def-graph","def-image":"functions.html#def-image","def-indexed-intersection":"sets.html#def-indexed-intersection","def-indexed-union":"sets.html#def-indexed-union","def-infinite-set":"functions.html#def-infinite-set","def-intersection":"sets.html#def-intersection","def-interval":"sets.html#def-interval","def-inverse-function":"functions.html#def-inverse-function","def-ordered-pair":"sets.html#def-ordered-pair","def-parse-tree":"expressions-algorithms.html#def-parse-tree","def-relation":"functions.html#def-relation","def-sequence":"functions.html#def-sequence","def-set":"sets.html#def-set","def-set-builder":"sets.html#def-set-builder","def-set-difference":"sets.html#def-set-difference","def-strict-subset":"sets.html#def-strict-subset","def-strict-superset":"sets.html#def-strict-superset","def-subset":"sets.html#def-subset","def-superset":"sets.html#def-superset","def-union":"sets.html#def-union","def-vacuous-truth":"sets.html#def-vacuous-truth","exm-algorithm":"expressions-algorithms.html#exm-algorithm","exm-cartesian-product":"sets.html#exm-cartesian-product","exm-collection":"sets.html#exm-collection","exm-complement":"sets.html#exm-complement","exm-composition":"functions.html#exm-composition","exm-countable-set":"functions.html#exm-countable-set","exm-de-morgan":"sets.html#exm-de-morgan","exm-domain-codomain-image":"functions.html#exm-domain-codomain-image","exm-elementwise-function":"functions.html#exm-elementwise-function","exm-empty-set":"sets.html#exm-empty-set","exm-expression":"expressions-algorithms.html#exm-expression","exm-extended-nonneg-reals":"sets.html#exm-extended-nonneg-reals","exm-finite-set":"functions.html#exm-finite-set","exm-function":"functions.html#exm-function","exm-graph":"functions.html#exm-graph","exm-indexed-union-intersection":"sets.html#exm-indexed-union-intersection","exm-interval":"sets.html#exm-interval","exm-inverse-function":"functions.html#exm-inverse-function","exm-no-known-algorithm":"expressions-algorithms.html#exm-no-known-algorithm","exm-parse-tree":"expressions-algorithms.html#exm-parse-tree","exm-relation":"functions.html#exm-relation","exm-sequence":"functions.html#exm-sequence","exm-set":"sets.html#exm-set","exm-set-builder":"sets.html#exm-set-builder","exm-set-operations":"sets.html#exm-set-operations","exm-strict-subset-superset":"sets.html#exm-strict-subset-superset","exm-subset":"sets.html#exm-subset","exm-vacuous-truth":"sets.html#exm-vacuous-truth","extended-non-negative-real-numbers":"sets.html#extended-non-negative-real-numbers","functions":"functions.html#functions","rem-cantor-diagonal":"functions.html#rem-cantor-diagonal","rem-cardinality-bars":"functions.html#rem-cardinality-bars","rem-elementwise-function-notation":"functions.html#rem-elementwise-function-notation","rem-empty-set-notation":"sets.html#rem-empty-set-notation","rem-expression-parse-tree":"expressions-algorithms.html#rem-expression-parse-tree","rem-function-as-set-of-pairs":"functions.html#rem-function-as-set-of-pairs","rem-function-expression-algorithm":"expressions-algorithms.html#rem-function-expression-algorithm","rem-graph-real-function":"functions.html#rem-graph-real-function","rem-image-range":"functions.html#rem-image-range","rem-infinity-arithmetic":"sets.html#rem-infinity-arithmetic","rem-inverse-not-reciprocal":"functions.html#rem-inverse-not-reciprocal","rem-naive-set":"sets.html#rem-naive-set","rem-no-known-algorithm":"expressions-algorithms.html#rem-no-known-algorithm","rem-strict-superset-subset":"sets.html#rem-strict-superset-subset","rem-subset-symbol":"sets.html#rem-subset-symbol","rem-superset-subset":"sets.html#rem-superset-subset","sec-further-reading":"sets.html#sec-further-reading","sets":"sets.html#sets","thm-de-morgan":"sets.html#thm-de-morgan","thm-empty-set-unique":"sets.html#thm-empty-set-unique","thm-empty-subset":"sets.html#thm-empty-subset","thm-interval-uncountable":"functions.html#thm-interval-uncountable","thm-subset-reflexive":"sets.html#thm-subset-reflexive"};
var id;
try {
id = decodeURIComponent(location.hash.slice(1));
} catch (e) {
return;
}
if (!Object.prototype.hasOwnProperty.call(map, id)) return;
var target = map[id];
var cut = target.indexOf("#");
var base = location.pathname.replace(/[^\\/]*$/, "");
location.replace(base + target.slice(0, cut) + location.search + target.slice(cut));
})();
</script>
```
# The pages {#sec-split-pages}
The definitions that were on this page are now on three pages:
- [Sets](sets.qmd):
sets, subsets, unions, intersections, complements, Cartesian products,
and the extended non-negative real numbers.
- [Functions](functions.qmd):
functions with their domains, codomains, and images,
composition, inverses, sequences, and countable sets.
- [Expressions and Algorithms](expressions-algorithms.qmd):
expressions, parse trees, and algorithms.