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The difference of two numbers $a$ and $b$ is a number $d$ such that
$b\!+\!d\;=\;a.$ 
The difference of $a$ (the minuend) and $b$ (the subtrahend) is denoted by $a\!\!b$.
The definition is similar for the elements $a,\,b$ of any additive Abelian group (e.g. of a vector space). The difference of them is always unique.
Note 1. Forming the difference of numbers (resp. elements), i.e. subtraction, is in a certain sense converse to the addition operation:
$(x\!+\!y)\!\!y\;=\;x$ 
Note 2. As for real numbers, one may say that the difference between $a$ and $b$ is $a\!\!b$ (which is the same as $b\!\!a$); then it is always nonnegative. For all complex numbers, such a phrase would be nonsense.
Some identities

$b\!+\!(a\!\!b)\;=\;a$

$a\!\!b\;=\;a\!+\!(b)$

$(a\!\!b)\;=\;b\!\!a$

$n(a\!\!b)\;=\;na\!\!nb\quad(n\in\mathbb{Z})$

$a\!\!a\;=\;0$
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