Negation
The negative version of a positive number is referred to as its negation. For example, −3 is the negation of the positive number 3. The sum of a number and its negation is equal to zero:
- 3 + −3 = 0.
That is, the negation of a positive number is the additive inverse of the number.
Using algebra, we may write this principle as an algebraic identity:
- x + −x = 0.
This identity holds for any positive number x. It can be made to hold for all real numbers by extending the definition of negation to include zero and negative numbers. Specifically:
- The negation of 0 is 0, and
- The negation of a negative number is the corresponding positive number.
For example, the negation of −3 is +3. In general,
- −(−x) = x.
The absolute value of a number is the non-negative number with the same magnitude. For example, the absolute value of −3 and the absolute value of 3 are both equal to 3, and the absolute value of 0 is 0.
Read more about this topic: Negative Number
Famous quotes containing the word negation:
“Friendship, according to Proust, is the negation of that irremediable solitude to which every human being is condemned.”
—Samuel Beckett (1906–1989)
“I am firmly opposed to the government entering into any business the major purpose of which is competition with our citizens ... for the Federal Government deliberately to go out to build up and expand ... a power and manufacturing business is to break down the initiative and enterprise of the American people; it is the destruction of equality of opportunity amongst our people, it is the negation of the ideals upon which our civilization has been based.”
—Herbert Hoover (1874–1964)
“We make a mistake forsaking England and moving out into the periphery of life. After all, Taormina, Ceylon, Africa, America—as far as we go, they are only the negation of what we ourselves stand for and are: and we’re rather like Jonahs running away from the place we belong.”
—D.H. (David Herbert)