The positive is usually explained to that the number under consideration is greater than zero.  Without the relationMathworldPlanetmath>”, the positivity of () numbers may be defined specifying which numbers of a given number kind are positive, e.g. as follows.

  • In the set of the integers, all numbers obtained from 1 via additionPlanetmathPlanetmath are positive.

  • In the set of the rationals, all numbers obtained from 1 via addition and division are positive.

  • In the set of the real numbers, the numbers defined by the equivalence classesMathworldPlanetmathPlanetmath of non-zero decimal sequencesMathworldPlanetmath are positive; these sequences (decimal expansions) consist of natural numbersMathworldPlanetmath from 0 to 9 as digits and a single decimal point (where two decimal sequences are equivalentMathworldPlanetmathPlanetmathPlanetmath if they are identical, or if one has an infiniteMathworldPlanetmath tail of 9’s, the other has an infinite tail of 0’s, and the leading portion of the first sequence is one lower than the leading portion of the second).

For example, 1+1+1 is a positive integer, 1+11+1+1+1+1 is a positive rational and  5.15115111511115 is a positive real number.

If a is positive and  a+b=0, then the opposite number b is negative.

The sets of positive integers, positive rationals, positive (real) algebraic numbersMathworldPlanetmath and positive reals are closed under addition and multiplication, so also the set of positive even numbersMathworldPlanetmath.

Title positive
Canonical name Positive
Date of creation 2013-03-22 14:35:05
Last modified on 2013-03-22 14:35:05
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 19
Author pahio (2872)
Entry type Definition
Classification msc 06F25
Classification msc 11B99
Classification msc 00A05
Synonym greater than zero
Defines negative