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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Null set question

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