RxR, the Cartesian product, is the set of all pairs, (x,y), where each of x and y is in R. T: R x R->R means that T is a function that, to every such pair, (x,y), assigns a member of R.Niles said:Homework Statement
Hi all.
If I have a set R and a function T, then what does the following mean: T: R x R -> R?
No, not if by "all elements in A are equal to all elements in B" you mean they are the same set. [itex]A \subset A[/itex] means that all elements of A are in B, but there are some elements of B that are not in A. [itex]A\subseteq B[/itex] includes the possibility that there are no elements of B that are not in A- the possiblility that A= B.Also, when I have a set A and a set B, then does the following mean that all elements in A are equal to all elements in B? A [itex]\subseteq[/itex] B
A set is a collection of distinct objects or elements. These objects can be anything from numbers, letters, to even complex mathematical expressions. Sets are often denoted by curly braces and each element is separated by a comma.
A set is a collection of elements, while a subset is a set that contains elements from another set. In other words, all elements in a subset are also found in the original set, but the original set may contain additional elements.
The cardinality of a set is the number of elements in the set. It is denoted by |S|, where S is the set. For example, if a set S = {1, 2, 3}, then |S| = 3.
The union of two sets, denoted by ∪, is the set of all elements that are in either set. The intersection of two sets, denoted by ∩, is the set of all elements that are in both sets. In other words, the union includes all elements from both sets, while the intersection only includes elements that are common to both sets.
An element refers to an individual object or value within a set, while a member of a set refers to the set itself. For example, in the set A = {1, 2, 3}, 1 is an element of the set, while A is a member of the set of all sets.