Sets & Notation: Homework Explained

[Niles]

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?

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

 

[HallsofIvy]

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?

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.

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

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.

 

[Niles]

Thank you. Two very good answers for two questions.

That cleared things up.