The discussion clarifies the notation and meaning of functions and set relationships in set theory. Specifically, T: R x R -> R indicates that the function T maps pairs of elements from set R to a single element in R, exemplified by T(x,y) = x + y for real numbers. Additionally, the notation A ⊆ B signifies that all elements of set A are contained within set B, but does not imply that A and B are identical; A ⊂ B indicates that A is a proper subset of B, meaning B contains elements not found in A.
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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