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Including 0, the set has a semiring structure (0 being the additive identity), known as the probability semiring; taking logarithms (with a choice of base giving a logarithmic unit) gives an isomorphism with the log semiring (with 0 corresponding to ), and its units (the finite numbers, excluding ) correspond to the positive real numbers.
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. A number is strictly negative if ...
Positive numbers: Real numbers that are greater than zero. Negative numbers: Real numbers that are less than zero. Because zero itself has no sign, neither the positive numbers nor the negative numbers include zero. When zero is a possibility, the following terms are often used: Non-negative numbers: Real numbers that are greater than or equal ...
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number.
Less than or equal to: ... Equivalently, if x is a positive real number, there is a positive integer n such that < <. Every positive real number x ...
The square root of 2 (approximately 1.4142) is the positive real number that, when multiplied by itself or squared, equals the number 2.It may be written in mathematics as , or /, and usually written as sqrt(2) in computer programming.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
If b is a positive real algebraic number, and x is a rational number, then b x is an algebraic number. This results from the theory of algebraic extensions . This remains true if b is any algebraic number, in which case, all values of b x (as a multivalued function ) are algebraic.