Opposite – Wikipedia, the free encyclopedia

In mathematics, the opposite (The symmetric for sum, The inverse additive) of a number

n{displaystyle n,}

is the number that, added with

n{displaystyle n,}

, gives zero. The additive inverse of

n{displaystyle n,}

is denoted

n{displaystyle -n,}

In our everyday language « opposite » would be equivalent to « opposite ».

Arithmetically, it can be calculated by multiplying by

1{displaystyle -1,}

, that is to say,

n=1×n{displaystyle -n=-1times n}

. Algebraically speaking, the opposite of an element of a group is its element symmetric with respect to the binary operation « 

+{displaystyle +,}

« (when using additive notation).

For example:

  • The opposite of
  • The opposite of

So, for the example above,

(0,3)=0,3{displaystyle -(-0,3)=0,3,}

.

Sets of numbers in which each element has opposites:

Sets of numbers without opposites:

Note that the integers are constructed from the natural numbers to which the opposites are formally added.

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