\(\DeclarePairedDelimiterX{\Set}[2]{\{}{\}}{#1 \nonscript\;\delimsize\vert\nonscript\; #2}\) \( \DeclarePairedDelimiter{\set}{\{}{\}}\) \( \DeclarePairedDelimiter{\parens}{\left(}{\right)}\) \(\DeclarePairedDelimiterX{\innerproduct}[1]{\langle}{\rangle}{#1}\) \(\newcommand{\ip}[1]{\innerproduct{#1}}\) \(\newcommand{\bmat}[1]{\left[\hspace{2.0pt}\begin{matrix}#1\end{matrix}\hspace{2.0pt}\right]}\) \(\newcommand{\barray}[1]{\left[\hspace{2.0pt}\begin{matrix}#1\end{matrix}\hspace{2.0pt}\right]}\) \(\newcommand{\mat}[1]{\begin{matrix}#1\end{matrix}}\) \(\newcommand{\pmat}[1]{\begin{pmatrix}#1\end{pmatrix}}\) \(\newcommand{\mathword}[1]{\mathop{\textup{#1}}}\)
Needs:
Set Numbers
Natural Sums
Needed by:
Number of Set Products
Set Numbers and Arithmetic
Links:
Sheet PDF
Graph PDF
Wikipedia

Number of Disjoint Unions

Result

We call two sets $A$, $B$ disjoint or non-overlapping1 if $A \cap B = \varnothing$.

Suppose $A$ and $B$ are disjoint finite sets. Then $\num{A \cup B} = \num{A} + \num{B}$
This is often called the addition principle or the rule of sum.
  1. Future sheets may move this definition elsewhere. ↩︎
Copyright © 2023 The Bourbaki Authors — All rights reserved — Version 13a6779cc About Show the old page view