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## Main Question or Discussion Point

Here's something else about sets I'm trying to get right. The empty set is a set that contains nothing, written as [tex]\phi[/tex] = {}. It's called an empty set, so it is a set. Every set contains the empty set, right? Is there such a notion as an empty element? That doesn't sound right to me.

Normally we distinguish between an element and the set containing that single element, correct? But if the empty set is nothing (or the set that contains nothing) then the set {[tex]\phi[/tex]} = {} = [tex]\phi[/tex]. Is it proper to say that the empty set and it's power sets are the same? What would that make the cardinality of the empty set, simply zero?

Normally we distinguish between an element and the set containing that single element, correct? But if the empty set is nothing (or the set that contains nothing) then the set {[tex]\phi[/tex]} = {} = [tex]\phi[/tex]. Is it proper to say that the empty set and it's power sets are the same? What would that make the cardinality of the empty set, simply zero?