empty set


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Related to empty set: Infinite set

empty set

Mathematics
The set that has no members or elements.
References in periodicals archive ?
[1] Let X be a non empty set, then A = {(x, [[mu].sub.A] (x)) : x [member of] X} is called a fuzzy set on X, where [[mu].sub.A](x) [member of] [0, 1] is the degree of membership function of each x [member of] X to the set A.
Tenders are invited for F.G.I.No.1,Mk-I Yellow Empty Set
It is possible that the set f(x) is the empty set. The effective domain of this function is the set of the x [member of] X such that f(x) [not equal to] [empty set].
It is never precisely clear whether she was born there and emigrated to Mexico, but the empty set, the nothingness, at the core of her story finds its roots there.
(a) ([x.sub.1], [x.sub.1]) is the empty set [empty set], which is the open internal set of [x.sub.1];
For x [member of] X, let [P.sub.A] (x) denote the set of best approximations to x in A (possibly empty set).
In this proof, the B constructs are prefixed by "b_", and "b_empty", "b_BIG", "b_in", "b_eq", and "b_drest" respectively represent the empty set [empty set], the set BIG (which is an infinite set, mostly only used to build natural numbers in the foundational theory), the membership operator "[member of]", the (extensional) equality "=", and the domain restriction construct "[??]".
They even sneaked on to the empty set and sat in Cowell's judge's seat.
Then the iteration [T.sup.[n+1]] = Z x SET([T.sup.[n]]) can be seen to converge to the class of rooted labeled trees, starting with [T.sup.[0]] the empty set. For any complex [alpha] with [absolute value of [alpha]] < [e.sup.-1], the corresponding numerical iteration [t.sup.[0]] = 0, [t.sup.[n + 1]] = [alpha]exp([t.sup.[n]]) converges to the value T([alpha]) = -W (-[alpha]) of the generating series of rooted labeled trees (W is the Lambert W function).
Let us consider a non- empty set E = {[e.sub.1], [e.sub.2], [e.sub.3]}.
A set that contains no elements is called the empty set. The set of existing tooth fairies or gods can be described as the empty set.
Then, there is [empty set] = {}, an empty set that contains no elements at all; and there is U, a universal set that contains all elements.