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  2. Opposite ring - Wikipedia

    en.wikipedia.org/wiki/Opposite_ring

    Two rings R 1 and R 2 are isomorphic if and only if their corresponding opposite rings are isomorphic. The opposite of the opposite of a ring R is identical with R, that is (R op) op = R. A ring and its opposite ring are anti-isomorphic. A ring is commutative if and only if its operation coincides with its opposite operation. [2]

  3. Additive inverse - Wikipedia

    en.wikipedia.org/wiki/Additive_inverse

    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]

  4. Anticommutative property - Wikipedia

    en.wikipedia.org/wiki/Anticommutative_property

    Subtraction is an anticommutative operation because commuting the operands of a − b gives b − a = −(a − b); for example, 2 − 10 = −(10 − 2) = −8. Another prominent example of an anticommutative operation is the Lie bracket.

  5. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Ternary: The base-three numeral system with 0, 1, and 2 as digits. Quaternary: The base-four numeral system with 0, 1, 2, and 3 as digits. Hexadecimal: Base 16, widely used by computer system designers and programmers, as it provides a more human-friendly representation of binary-coded values.

  6. Elementary mathematics - Wikipedia

    en.wikipedia.org/wiki/Elementary_mathematics

    A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred to by using ordinal numbers, as in fourth root, twentieth root, etc. For example: 2 is a square root of 4, since 2 2 = 4. −2 is also a square root of 4, since (−2) 2 = 4.

  7. Dual number - Wikipedia

    en.wikipedia.org/wiki/Dual_number

    In algebra, the dual numbers are a hypercomplex number system first introduced in the 19th century. They are expressions of the form a + bε , where a and b are real numbers , and ε is a symbol taken to satisfy ε 2 = 0 {\displaystyle \varepsilon ^{2}=0} with ε ≠ 0 {\displaystyle \varepsilon \neq 0} .

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