What is order in $n-$tuple? $n-$tuple is a sequence (or ordered list) of n elements, where n is a non-negative integer. 
By sequence i understand a pattern either increasing or decreasing.
But if  $(2, 7, 4, 1, 7)$ is an example of $5-$tuple, then where is the order here ? It is neither increasing nor decreasing.
 A: The word "order", when it comes to tuples and sequences, does not refer to any pattern found in the numbers contained in the tuple. The elements of a tuple do not necessarily have to be increasing or decreasing. "Order" refers to the defining characteristic of a tuple, which is that each element has a distinct position inside the tuple.
For example, $(1,2,3)$ and $(1,3,2)$ are both valid tuples, but the positions of $2$ and $3$ are swapped, so the tuples are not equal. This is different from sets, where $\{1,2,3\}$ and $\{1,3,2\}$ would be the same set since they contain the same elements.
A: One useful definition of an $n$-tuple is that it's a function
$$
s: \{1, 2, 3, \ldots, n\} \to \mathbb R
$$
This defined tuples in terms of something familiar (functions), and it's completely clear how it differs from the 
$$
\{
s(1), \ldots, s(n)\}
$$
which might contain only a single element, if $s$ were a constant-function. 
As for the whole "increasing/decreasing" thing, as @Regret says, there's no requirement that a sequence be increasing or decreasing. They typically are, but not always. 
(By the way, the "function" definition is a little circular, in that functions are defined in terms of ordered pairs...which is a problem. So let me say that an ordered pair $(a, b)$ is the set $\{\{a\}, \{a, b\}\}$ just to start the recursion, so to speak.)
