Given set $ A = emptyset $ what is $|A|$? I simply learned around sets this particular day in course and I"m unsure exactly how to answer this.


$A=\emptyset$ is a set containing one facet. That element is itself likewise a set, however this is irappropriate.

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Note the distinction between $A=\emptyset$, $B=emptyset$, and $C=\emptyset\$. These are all various sets. $A$ is the set containing the emptycollection. $B$ is the emptycollection, and $C$ is the collection containing the set containing the empty collection.

Cardinality of a finite set is ssuggest the number of aspects had in the collection, so in this instance $|A|=1$

Similarly, $|C|=1$ and also $|B|=0$ for the other examples I included over.


In a way it is the start of the building of herbal numbers (cardinalities of finite sets)

0=|∅ |,1=|∅|,2=|∅ ,∅ |,3=|∅ ,∅ ,∅ ,∅ |,...

as you watch the initially collection (in between |.|) has no elements, the second one has actually one facet, the 3rd one has 2 distinct facets as the empty set and the collection whose only aspect is an empty collection are different. The (generally confusing) ... just adds the nested braces.


I"m assuming the obstacle is from the imprecision of language, it might sound like the "collection of the empty set" is the exact same as an empty collection kind of like exactly how a double-negative in English deserve to really mean a negative. Just call "the empty set" something else to make it less confutilizing. Say it"s "the special set" rather, something much less intuitively transitive or inheritable than emptiness, dedetailed by $S$ instead of $emptyset$. Then $A = S$. How many elements does $A$ have?


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Suppose that $A$ is a collection such that $|A| = m$. What is $| le 1 |$?
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