Bifalgorithm post · Brisk · Chapter 1

How are all the subsets of a set formed?

How are all the subsets of a set formed? (Brisk · Chapter 1) — "It might seem strange to talk about “all of the possible subsets” — when I first learned this s…

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Les sous-ensembles possibles d’un ensemble sont déterminés par l’inclusion ou l’exclusion de chacun de ses éléments.
On peut d’abord croire que le nombre de sous-ensembles est illimité.
Pour chaque élément, il existe deux choix : l’inclure ou l’exclure.
Dans l’exemple, A contient Dad et Lizzy.
Inclure Dad et Lizzy.
Inclure Dad, mais exclure Lizzy.
Inclure Lizzy, mais exclure Dad.
Exclure Dad et Lizzy, ce qui donne le sous-ensemble ∅.
Ces quatre possibilités constituent tous les sous-ensembles de A.
Ainsi, P(A) contient les quatre sous-ensembles obtenus.

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How are all the subsets of a set formed?

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"It might seem strange to talk about “all of the possible subsets” — when I first learned this stuff, I remember thinking at first that there would be no limit to the number of subsets you could make from a set. But of course there is. To create a subset, you can either include, or exclude, each one of the original set’s members. In A’s case, you can either (1) include both Dad and Lizzy, or (2) include Dad but not Lizzy, or (3) include Lizzy but not Dad, or (4) exclude both, in which case your subset is ∅. Therefore, P(A) includes all four of those subsets."

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