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empty set

null set
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03-00 no label found65H05 no label found65H10 no label found


Can you explain me why an empty set is a subset of every other set?
By definition, or is there a demonstration, or it's a convention?
And since any two empty sets are equal, do you allow me to say that every man that is also a woman is a subset of irrational numbers?

A is a subset of B, if any any element of A is also an element of B.
If A = {}, it fulfils the above requirement; since A is empty, the requirement is empty, we require nothing! (Try to find some element of {} not belonging to B !)

What I want to point out is that you must explicitly mention when empty set is an element of a set. The set of my customers is sometimes big but, unfortunately, it's happen to be empty occasionally. But the set of my actions in my office can't be empty, even if I fall asleep sometimes: at least, I get older every second.

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