What are ordered tuples?

Question

I've been asked to explain the concepts of relations and I'm unable to find what Ordered Tuples are on the internet.

Could the answer please be given in the most basic form as I'm not brilliant at Maths.

Thanks in advance.

Answer 1

An ordered tuple is a collection of stuff with a prescribed order. Compare this to the notion of a set, where no order is specified.

So, for example, the sets $$ \{1,2,3\}, \{2,3,1\},\{1,1,1,2,2,3\} $$ are all considered to be the "same set", but written differently. However, the tuples (or ordered tuples) given by $$ (1,2,3),(2,3,1),(1,1,1,2,2,3) $$ are distinct objects.

It is important to consider tuples when thinking about functions or relations. In particular, coordinates should be tuples rather than sets since, for example, the points $(0,1)$ and $(1,0)$ are distinct objects. Once we know what coordinates are, we can think of a function as the set of all coordinates $(x,f(x))$ that would be on the graph.

Functions are a particular kind of relation, so perhaps this will be a helpful guide to figuring things out more generally.