1
$\begingroup$

If a triplet or any set is ordered say $(x,y,z)$ does that mean that $x\leq y\leq z$ Or can the variables be in any order?

2 Answers 2

2

Let's give an example:

How many ordered pairs of natural numbers whose sum is $4$ are there? There are $(1,3)$, $(2,2)$ and $(3,1)$. So there are three such ordered pairs.

How many unordered pairs of natural numbers whose sum is $4$ are there? Now we do not distinguish between $(1,3)$ and ($3,1)$, so now there are only two such unordered pairs.

When talking of unordered pairs, we have $(a,b)=(b,a)$, when talking of orderd pairs, we have $(a,b)\ne (b,a)$ unless $a=b$. (Beware of the notation $(a,b)$ I used for unordered pairs as it is usually reserved for ordered pairs; one might write $\{a,b\}$ for unordered, but then one should mention that this is not a set, but rather a multiset).

0

The triples $a$,$b$ and $c$ can be in any order.(in this case, there are $3!=6$ of them)