# Sets and notation

1. Nov 8, 2009

### Niles

1. The problem statement, all variables and given/known data
Hi all.

If I have a set R and a function T, then what does the following mean: T: R x R -> R?

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 $\subseteq$ B

2. Nov 8, 2009

### HallsofIvy

Staff Emeritus
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.

Operations are often represented that way. For example, if R is the set of real numbers, R x R is the set of pairs of real numbers and addition, "+", assigns a single number to every pair of numbers: T(x,y)= x+ y so 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. $A \subset A$ means that all elements of A are in B, but there are some elements of B that are not in A. $A\subseteq B$ includes the possibility that there are no elements of B that are not in A- the possiblility that A= B.

3. Nov 8, 2009

### Niles

Thank you. Two very good answers for two questions.

That cleared things up.