TITLE: Name for $(1-x)$?
QUESTION [14 upvotes]: The multiplicative inverse of $x$ is $\frac{1}{x}$, 
and the additive inverse of $x$ is $-x$,
is there a similar term for $(1-x)$?

REPLY [6 votes]: I'd call it a complement or a negation.  You don't need to stand all that close to probability for these names to seem meaningful, in my opinion.  If we have 0 as indicating falsity, and 1 as indicating truth, then the negation of a proposition x has truth value of (1-x).  The same holds if we have 1 as indicating falsity, and 0 as indicating truth.  In fuzzy logic, which has truth values of the unit interval [0, 1], (1-x) also comes as the fuzzy complement most commonly considered.
Also, consider classical or crisp sets under their characteristic function representation.  The characteristic function assigns 1 to each element of the universal set which belongs to the subset under consideration, and 0 to each element of the universal set which does not belong to the subset under consideration.  For example, if we have {a, b, c, d} as our universal set, and {a, b} as the subset under consideration, the characteristic function assigns 1 to a, 1 to b, 0 to c, and 0 to d, or equivalently
{(a, 1), (b, 1), (c, 0), (d, 0)}.  Now, the complement of {a, b} for this universal set equals {c, d}.  Well, (1-x) on the values defined by the characteristic function for 
{a, b}={(a, 1), (b, 1), (c, 0), (d, 0)} gives us {(a, 0), (b, 0), (c, 1), (d, 1)}={c, d} the complement of {a, b}.  This does generalize also such that (1-x) here always gives us the complement of the subset under consideration.