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Anti addition is in direct contrast to syn addition. In anti addition, two substituents are added to opposite sides (or faces) of a double bond or triple bond, once again resulting in a decrease in bond order and increase in number of substituents. The classical example of this is bromination (any halogenation) of alkenes. [5]
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]
In addition, the symbol + represents the operation of addition, which results in a sum, while the symbol − represents subtraction, resulting in a difference. [1] Their use has been extended to many other meanings, more or less analogous. Plus and minus are Latin terms meaning 'more' and 'less', respectively.
Addition and multiplication are commutative in most number systems, and, in particular, between natural numbers, integers, rational numbers, real numbers and complex numbers. This is also true in every field. Addition is commutative in every vector space and in every algebra. Union and intersection are commutative operations on sets.
Such reactions are said to be anti-Markovnikov, since the halogen adds to the less substituted carbon, the opposite of a Markovnikov reaction. The anti-Markovnikov rule can be illustrated using the addition of hydrogen bromide to isobutylene in the presence of benzoyl peroxide or hydrogen peroxide. The reaction of HBr with substituted alkenes ...
The most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse. An operation of arity zero, or nullary operation, is a constant.
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
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 R.