positive
The positive is usually explained to that the number under consideration is greater than zero. Without the relation^{} “$>$”, the positivity of () numbers may be defined specifying which numbers of a given number kind are positive, e.g. as follows.
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In the set $\mathbb{R}$ of the real numbers, the numbers defined by the equivalence classes^{} of nonzero decimal sequences^{} are positive; these sequences (decimal expansions) consist of natural numbers^{} from 0 to 9 as digits and a single decimal point (where two decimal sequences are equivalent^{} if they are identical, or if one has an infinite^{} 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, $\frac{1+1}{1+1+1+1+1}$ is a positive rational and $5.15115111511115\mathrm{\dots}$ 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 numbers^{} and positive reals are closed under addition and multiplication, so also the set of positive even numbers^{}.
Title  positive 

Canonical name  Positive 
Date of creation  20130322 14:35:05 
Last modified on  20130322 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 