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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.

Jarkerwastaken
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  • You can think of an ordered tuple as a vector whose entries do not have to be numbers.Does that help? If you don't know what a vector is, just think about a list. – Ethan Bolker Feb 24 '16 at 13:23
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    It would help to know what this is for. Is it requiring a formal definition using set theory, or an informal explanation? – Thomas Andrews Feb 24 '16 at 13:25
  • $(a,b)={{a},{a,b}}$ – Rasmus Erlemann Feb 24 '16 at 13:29
  • You might start with "ordered pair", and then move on to "ordered triple", for which there are lots of entries on the internet. If you get those, you might then be able to generalize yourself to "ordered 4-tuples", "ordered 5-tuples", and then to ordered tuples in complete generality. – Lee Mosher Feb 24 '16 at 13:51

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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.

Ben Grossmann
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