# 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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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.

That's great, yes the 3rd question was just blathering on but the answer to the second question answered what I meant.

Thanks a lot, have a good day :)