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−1 : ウィキペディア英語版
−1

In mathematics, −1 is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less than 0.
Negative one bears relation to Euler's identity since e^ = -1.\!
In software development, −1 is a common initial value for integers and is also used to show that a variable contains no useful information.
Negative one has some similar but slightly different properties to positive one.〔(Mathematical analysis and applications )
By Jayant V. Deshpande, ISBN 1-84265-189-7〕
==Algebraic properties==
Multiplying a number by −1 is equivalent to changing the sign on the number. This can be proved using the distributive law and the axiom that 1 is the multiplicative identity: for x real, we have
:x+(-1)\cdot x=1\cdot x+(-1)\cdot x=(1+(-1))\cdot x=0 \cdot x=0
where we used the fact that any real x times 0 equals 0, implied by cancellation from the equation
:0\cdot x=(0+0)\cdot x=0\cdot x+0\cdot x \,
In other words,
:x+(-1)\cdot x=0 \,
so (−1) · ''x'' is the arithmetic inverse of ''x'', or −''x''.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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