Search results
Results from the WOW.Com Content Network
In mathematics real is used as an adjective, meaning that the underlying field is the field of the real numbers (or the real field). For example, real matrix, real polynomial and real Lie algebra. The word is also used as a noun, meaning a real number (as in "the set of all reals").
In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, [2] and reductio ad impossibile. [ 3 ] A mathematical proof employing proof by contradiction usually proceeds as follows:
The real values of individual goods or commodities may rise or fall against each other, in relative terms, but a representative commodity bundle as a whole retains its real value as a constant from one period to the next. Real values can for example be expressed in constant 1992 dollars, with the price level fixed 100 at the base date.
In a vector space, the additive inverse −v (often called the opposite vector of v) has the same magnitude as v and but the opposite direction. [9] In modular arithmetic, the modular additive inverse of x is the number a such that a + x ≡ 0 (mod n) and always exists. For example, the inverse of 3 modulo 11 is 8, as 3 + 8 ≡ 0 (mod 11). [10]
In addition to the sign of a real number, the word sign is also used in various related ways throughout mathematics and other sciences: Words up to sign mean that, for a quantity q, it is known that either q = Q or q = −Q for certain Q. It is often expressed as q = ±Q. For real numbers, it means that only the absolute value |q| of
The real absolute value function is continuous everywhere. It is differentiable everywhere except for x = 0. It is monotonically decreasing on the interval (−∞, 0] and monotonically increasing on the interval [0, +∞). Since a real number and its opposite have the same absolute value, it is an even function, and is hence not invertible.
Hyperphantasia is the condition of having extremely vivid mental imagery. [1] It is the opposite condition to aphantasia, where mental visual imagery is not present. [2] [3] The experience of hyperphantasia is more common than aphantasia [4] [5] and has been described as being "as vivid as real seeing". [4]
Antiphrasis is the rhetorical device of saying the opposite of what is actually meant in such a way that it is obvious what the true intention is. [1] Some authors treat and use antiphrasis just as irony, euphemism or litotes. [2] When the antiphrasal use is very common, the word can become an auto-antonym, [3] having opposite meanings ...