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Context from my School Textbook.

A set containing no elements is called the empty set or null set or void set. Reading Notation : The empty set or null set or void set is denoted by the symbol $\emptyset$ or $\{ \}$.

The concept of empty set plays a key role in the study of sets just like the role of the number zero in the study of number system. Think and answer! What is $n(\emptyset)$?

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closed as unclear what you're asking by Andrés E. Caicedo, user223391, Leucippus, Alex Wertheim, hardmath Oct 4 '17 at 4:13

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  • $\begingroup$ What does $n\{\}$ denote? Cardinality? $\endgroup$ – JohnColtraneisJC Oct 3 '17 at 17:37
  • $\begingroup$ That's where I'm confused. $\endgroup$ – Harish Raja Oct 3 '17 at 17:38
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    $\begingroup$ If you were to go just a page or two before, I'm sure they would have very explicitly stated what $n(\cdot)$ represents. If you had taken the time to read that, you wouldn't have needed to ask this question. Downvoting for lack of research effort. $\endgroup$ – JMoravitz Oct 3 '17 at 17:44
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Without additional information, I can only guess. But I think it's likely that $n(A)$, for a given set $A$, is the number of elements of $A$. Since the empty set $\emptyset$ has no elements, we thus have $n(\emptyset) = 0$.

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  • $\begingroup$ If set A has no elements then it can be written A = { } or A = Φ. Can Φ be treated as set like A written as Φ = { } $\endgroup$ – Harish Raja Oct 3 '17 at 17:44
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    $\begingroup$ @HarishRaja of course. Why wouldn't it? $\endgroup$ – JMoravitz Oct 3 '17 at 17:45
  • $\begingroup$ So, I understand like, if any set ,For example, set X and Y have no elements. Then the set X = Y = Φ = { } where Φ is the other name of set X and Y. $\endgroup$ – Harish Raja Oct 3 '17 at 17:48
  • $\begingroup$ Yes, two sets $X,Y$ are equal if and only if they have the same element. Hence there is a unique empty set - the set with no elements. $\endgroup$ – Stefan Mesken Oct 3 '17 at 17:50
  • $\begingroup$ Is it usual to n({ }) = Φ ? $\endgroup$ – Harish Raja Oct 3 '17 at 17:52

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