Ads
related to: additive inverse worksheet
Search results
Results From The WOW.Com Content Network
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]
For instance, to solve the inequality 4x < 2x + 1 ≤ 3x + 2, it is not possible to isolate x in any one part of the inequality through addition or subtraction. Instead, the inequalities must be solved independently, yielding x < 1 / 2 and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < 1 / 2 .
The product-to-sum identities [28] or prosthaphaeresis formulae can be proven by expanding their right-hand sides using the angle addition theorems. Historically, the first four of these were known as Werner's formulas , after Johannes Werner who used them for astronomical calculations. [ 29 ]
Subtraction is the inverse of addition. [1] The function whose value for any real or complex argument is the additive inverse of that argument. For example, if x = 3, then −x = −3, but if x = −3, then −x = +3. Similarly, −(−x) = x. A prefix of a numeric constant. When it is placed immediately before an unsigned number, the ...
Under addition, a ring is an abelian group, which means that addition is commutative and associative; it has an identity, called the additive identity, and denoted 0; and every element x has an inverse, called its additive inverse and denoted −x. Because of commutativity, the concepts of left and right inverses are meaningless since they do ...
Therefore, one would say that multiplication distributes over addition. This basic property of numbers is part of the definition of most algebraic structures that have two operations called addition and multiplication, such as complex numbers, polynomials, matrices, rings, and fields.
The additive inverse of a number is unique, as is shown by the following proof. As mentioned above, an additive inverse of a number is defined as a value which when added to the number yields zero. Let x be a number and let y be its additive inverse. Suppose y′ is another additive inverse of x.
In a sense, subtraction is the inverse of addition. That is, c = a − b if and only if c + b = a. In words: the difference of two numbers is the number that gives the first one when added to the second one. Subtraction follows several important patterns. It is anticommutative, meaning that changing the order changes the sign of the answer.