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In mathematics, specifically abstract algebra, the opposite of a ring is another ring with the same elements and addition operation, but with the multiplication performed in the reverse order. More explicitly, the opposite of a ring ( R , +, ⋅ ) is the ring ( R , +, ∗) whose multiplication ∗ is defined by a ∗ b = b ⋅ a for all a , b ...
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. [11] 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). [12]
This polynomial is irreducible over the rationals and so the three cosines are conjugate algebraic numbers. Likewise, tan 3 π / 16 , tan 7 π / 16 , tan 11 π / 16 , and tan 15 π / 16 satisfy the irreducible polynomial x 4 − 4x 3 − 6x 2 + 4x + 1 = 0, and so are conjugate algebraic integers. This is the ...
For example, − (−3) = 3 because the opposite of an opposite is the original value. Negative numbers are usually written with a minus sign in front. For example, −3 represents a negative quantity with a magnitude of three, and is pronounced and read as "minus three" or "negative three".
In mathematics, the concept of an inverse element generalises the concepts of opposite (−x) and reciprocal (1/x) of numbers.. Given an operation denoted here ∗, and an identity element denoted e, if x ∗ y = e, one says that x is a left inverse of y, and that y is a right inverse of x.
Algebraic number: Any number that is the root of a non-zero polynomial with rational coefficients. Transcendental number: Any real or complex number that is not algebraic. Examples include e and π. Trigonometric number: Any number that is the sine or cosine of a rational multiple of π.
An early occurrence of proof by contradiction can be found in Euclid's Elements, Book 1, Proposition 6: [7] If in a triangle two angles equal one another, then the sides opposite the equal angles also equal one another. The proof proceeds by assuming that the opposite sides are not equal, and derives a contradiction.
Quizlet is a multi-national American company that provides tools for studying and learning. [1] Quizlet was founded in October 2005 by Andrew Sutherland, who at the time was a 15-year old student, [ 2 ] and released to the public in January 2007. [ 3 ]
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