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The multiplicative identity of R[x] is the polynomial x 0; that is, x 0 times any polynomial p(x) is just p(x). [2] Also, polynomials can be evaluated by specializing x to a real number. More precisely, for any given real number r, there is a unique unital R-algebra homomorphism ev r : R[x] → R such that ev r (x) = r. Because ev r is unital ...
In mathematics, the additive inverse of an element x, denoted -x, [1] is the element that when added to x, yields the additive identity, 0. [2] In the most familiar cases, this is the number 0, but it can also refer to a more generalized zero element. In elementary mathematics, the additive inverse is often referred to as the opposite number.
The minus sign "−" signifies the operator for both the binary (two-operand) operation of subtraction (as in y − z) and the unary (one-operand) operation of negation (as in −x, or twice in −(−x)). A special case of unary negation occurs when it operates on a positive number, in which case the result is a negative number (as in −5).
Such an ambiguity can be mitigated by writing "x is strictly positive" for x > 0, and "x is non-negative" for x ≥ 0. (A precise term like non-negative is never used with the word negative in the wider sense that includes zero.) The word "proper" is often used in the same way as "strict".
A number is non-negative if it is greater than or equal to zero. A number is non-positive if it is less than or equal to zero. When 0 is said to be both positive and negative, [citation needed] modified phrases are used to refer to the sign of a number: A number is strictly positive if it is greater than zero.
Graphs of y = b x for various bases b: base 10, base e, base 2, base 1 / 2 . Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.
For example, the quotient can be defined to equal zero; it can be defined to equal a new explicit point at infinity, sometimes denoted by the infinity symbol; or it can be defined to result in signed infinity, with positive or negative sign depending on the sign of the dividend. In these number systems division by zero is no longer a special ...
For example, consider the set of negative real numbers (excluding zero). This set has no greatest element, since for every element of the set, there is another, larger, element. For instance, for any negative real number , there is another negative real number , which is greater. On the other hand, every real number greater than or equal to ...