cartesian products: Give ex. of set that cannot be expressed

[woolley]

Given two subsets A and B of R, recall that their Cartesian product A × B ⊂ R^2 is defined as A × B = {(a, b) : a ∈ A, b ∈ B} Give an example of a set X ⊂ R^2 that cannot be expressed as the Cartesian product of sets A, B ⊂ R.

 

[pka]

The empty-set is a subset of any set.

 

[daon]

Here's one: \(\displaystyle \{ \(x,y\) \,\, | \,\, x^2 + y^2 < 4}\).