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In the book 'A Course in modern mathematical physics' for Peter Szekeres. I read "an ordered $n$-tuple is a set in which the order of the elements must be specified." No problem till now , but just keep in mind its a 'set' but (special). In Wikipedia, I've seen that one of its properties is that: A tuple may contain multiple instances of the same element, so tuple $(1,2,2,3)\neq (1,2,3)$, but set $\{1,2,2,3\}=\{1,2,3\}$.

I understand that a tuple shows the order of the elements in a set; BUT its still a set , so what's the meaning of repeating the same element more than one time , what's the point of that?

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1 Answer

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An $n$-tuple is only a set for set theorists, since to them everything is a set.

For us ordinary mortals an $n$-tuple is a function $f:\>[n]\to X$, whereby $X$ is a predefined set. Such an $f$ is "datawise" completely determined in the form of the list $(x_1,x_2,\ldots, x_n)$ of its function values $x_k:=f(k)\in X$ $(1\leq k\leq n)$.

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