===== Maximal extension in a set =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $A$ ... set |
| @#55CCEE: context     | @#55CCEE: $a\in A$ |
| @#FFBB00: definiendum | @#FFBB00: $\mathrm{max}(a,A)\equiv\bigcup\{b\mid b\in A\land a\subseteq b\}$ |

==== Discussion ====
=== Idea ===
Given $a\in A$, the maximal extension $\mathrm{max}(a,A)$ is the largest set in $A$ which encompasses $a$.

=== Predicate ===
| @#EEEE55: predicate   | @#EEEE55: $x$ maximal in $X \equiv \mathrm{max}(x,X)=x$ |

=== Reference ===
==== Parents ====
=== Element of ===
[[Set universe]]