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:
“Michelangelo said to Pope Julius II, “Self negation is noble, self-culture is beneficent, self-possession is manly, but to the truly great and inspiring soul they are poor and tame compared to self-abuse.” Mr. Brown, here, in one of his latest and most graceful poems refers to it in an eloquent line which is destined to live to the end of time—”None know it but to love it, None name it but to praise.””
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“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)
“Friendship, according to Proust, is the negation of that irremediable solitude to which every human being is condemned.”
—Samuel Beckett (1906–1989)