# Binary in Real Analysis & Sets?

Hi, I have a few questions because I'm watching a lecture on real analysis & I'm a little bit unsure of a few things. I have them in point form for your convenience in answering.

1.
A (binary) relation R is a subset of AxB.

If (a,b) ε R then aRb
(from 2.30 in the video - no need to watch)

A & B are sets & AxB is the set "product" definition
AxB = {(a,b) : aεA & bεB}

which is a way of talking about an ordered pair, say on the Cartesian plane.

Is that correct so far?

I am wondering what it means to say "binary"? Does this refer to the fact that AxB results in two elements a & b?

2.Also, everytime AxA is specified in a book or somewhere, does that refer to an "ordered pair" i.e. RxR is a way to tell you that you are using an ordered pair e.g. (2,3) in the plane?

3.This tells you that you are taking the "set-product" of two subsets to ensure the legality of using an ordered pair?

4. $$R^3$$ This is the Euclidian 3-dimensional space, whenever an author mentions this does the author mean to specify that we are taking some sort of a "set-product", like an ordered triple?

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boboYO
1)binary relation means that it's a relation defined on 2 inputs. so yes, you are right.

2) AxB doesn't refer to a specific ordered pair. AxB denotes the SET of all ordered pairs, that have first element taken from the set A and the 2nd element taken from the set B.

3) not sure what you asking, AxB is a set (whose elements are ordered pairs).

4)Yes, when the author mentions this he means the set of all ordered triples with elements taken from R.