Terminology for splittings of a set into two parts I have a set of values $V$ that can be split by any combination $C$ of the elements $v$ that belongs to $V$. Order is not important and repetitions are not allowed.
For example, $V := \{1,2,3,4\}$ 
$C_0 \Rightarrow V_0:=\{1\}, V_1:=\{2,3,4\}$ 
$C_1 \Rightarrow V_0:=\{2\}, V_1:=\{1,3,4\}$  
$\vdots$  
$C_{13} \Rightarrow V_0:=\{2,3,4\}, V_1:=\{1\}$  
It turns out I can get all the possible splits of the set by evaluating only half of every allowed combinations.
I've written a function in C# that does this but I cannot find a name that describes exactly this scenario. 
Do this kind of math have a name, something like PartitionCombinations or something like that?
I'm not a mathematician at all. Sorry for everything from bad formatting, notation, explaining etc.
Thank you.
 A: In the terminology for partitions of a set, the nonempty subsets that belong to the partition (a set of sets) are called blocks, parts, or cells.  So one might refer to the constructed partitions here as partitions of a set with two parts.
However I call your attention to the list of 14 "splittings" given for the set $V=\{1,2,3,4\}$.  Because a partition is a set of subsets of $V$, we do not consider the first $C_0$ and last $C_{13}$ splittings to be different partitions.  That is, $V = V_0 \cup V_1$ for both "splittings", and the partition in both cases would be $\{\{1\},\{2,3,4\}\}$.
If you want to consider these as different solutions of your problem, you may want to invent your own term for what you are constructing.  Of course as you've already worked out, your splittings are determined by a choice of proper nonempty subset $\emptyset \subsetneq V_0 \subsetneq V$, forcing $V_1 = V\setminus V_0$.  My 2-part partitions of $V$ are only half as many, because the order of the subsets $V_0,V_1$ is neglected.
