What are the differences between empty set, zero set and null set?
If i'm right empty set and null set is the same which is {} but zero set is {0} ?
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The null set, also known as empty set, is the set containing no elements, denoted by $\emptyset$ or {}
The zero set of of a real-valued function f : X → R is the subset of X on which f(x) = 0.
Patricia
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+1. I would also add that we also see "null" used as an adjective, meaning "having measure zero". And, of course, there are non-empty sets which are null in this sense (which is why I never use "null set" to refer to the empty set). – Noah Schweber May 07 '16 at 23:27
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@NoahSchweber : I think https://en.wikipedia.org/wiki/Null_set is always a set of measure $0$ – reuns May 08 '16 at 00:04
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@user1952009 Sadly, that's not true - I've seen "the null set" used to refer to the empty set frequently. – Noah Schweber May 08 '16 at 00:06
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One could say that "zero set" is both defined and declared, but "null set" and "empty set" are only defined.
Jerry
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