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What is "Containment order"? Could I get a friendly explanation?
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containmentorderwhatcouldgetfriendlyexplanation
Problem
Reading the Wikipedia page was a little dense for me. Can anyone offer a friendly explanation of what this means? It sounds like it saying that if you have two ordered collections, if they are "ordered by containment" then they will be in roughly the same order with each other?
Solution
I'll try a down to earth definition \ example:
When speaking of a set $X$, lets say $X=\{1,...,100\}$,
denote the subset $X_i = \{1,...,i\}$
It holds that $X_1\subseteq X_2\subseteq...\subseteq X_{100}$
So you could say there is a containment order over these subsets, because each subset contains the other in an order that I stated. This order came from, and connected to (and isomorphic to) the partial order of $1 \leq 2 \leq ... \leq 100$ or if you prefer more fomally, that $(X,\leq )$ is a poset.
When speaking of a set $X$, lets say $X=\{1,...,100\}$,
denote the subset $X_i = \{1,...,i\}$
It holds that $X_1\subseteq X_2\subseteq...\subseteq X_{100}$
So you could say there is a containment order over these subsets, because each subset contains the other in an order that I stated. This order came from, and connected to (and isomorphic to) the partial order of $1 \leq 2 \leq ... \leq 100$ or if you prefer more fomally, that $(X,\leq )$ is a poset.
Context
StackExchange Computer Science Q#86314, answer score: 4
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