What is the difference between ordered and unordered n-tuple? From browsing the internet so far I've came to the conclusion that an ordered tuple is something in which there is no repettion of the elments
Eg: An ordered 4-tuple is (1,2,3,4) or (5,3,1,7) i.e. no elements are repeated
But an unordered 4-tuple is something like this (1,2,2,3) or (7,1,4,1)
Is this a valid difference between an ordered and an unordered tuple? If yes then are there any other differences??
Thanks in advance.
 A: No, that's completely wrong.  Whether ordered or unordered, there may or may not be repetitions.  The correct distinction is that in an ordered tuple the order counts, and in an unordered tuple it doesn't.  So $(1,2,2,3)$ and $(2,1,2,3)$ are different as ordered $4$-tuples, but they are the same as unordered $4$-tuples.
A: Consider the Cartesian product to clarify things a little bit. 
The Cartesian product of two sets $A$ and $B$ is defined to be the set of all ordered pairs $(a,b)$ where $a\in A$ and $b\in B$. The Cartesian product is often written as
$$
A\times B = \{(a,b)\mid a\in A\space\text{and}\space b\in B\}.
$$
Thus, consider the Cartesian product when $A=\{1\}$ and $B=\{2\}$. We get $A\times B=\{(1,2)\}$. What about $B\times A$? We get $\{(2,1)\}$. For Cartesian products, $\{(1,2)\}\neq \{(2,1)\}$ because the pairs are ordered. $\color{red}{\text{The manner in which the entries appear matters}}$, as Robert Israel pointed out. 
The Cartesian product is concerned with $2$-tuples. The same reasoning may be applied to any $n$-tuple.
