Solution to give an example of a choice function on the collection. X = {{0.1},{2,3},{4,5}} - Sikademy
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give an example of a choice function on the collection. X = {{0.1},{2,3},{4,5}}

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Axiom of Choice.

Let X be a collection of nonempty sets. Then we can choose a member from each set in that collection. In other words, there exists a function f defined on X with the property that, for each set S in the collection, f(S) is a member of S.

The function f is then called a choice function.

For example, if X is the collection X =\{ \{{0,1\}} ,\{{2,3\}},\{{4,5\}}\}, then we can define f quite easily: just let f(S) be the smallest member of S.

Then the function that assigns 0 to the set \{{0,1\}}, 2 to \{{2,3\}}, and 4 to \{{4,5\}} is a choice function on X.

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