## notation - Does set $\mathbb{R}^+$ include zero? - Mathematics Stack

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** Does set $\mathbb{R}^+$ include zero? **

up vote 9 down vote favorite
*1*
I've been trying to find answer to this question for some time but in
every document I've found so far it's taken for granted that reader know
what $\mathbf â^+$ is.

notation number-systems

share|cite|improve this question
edited Nov 3 '10 at 1:05
Carl Mummert
50.7k594193
asked Aug 6 '10 at 9:03
AndrejaKo
450417

22

It depends on the choice of the person using the notation: sometimes it
does, sometimes it doesn't. It is just a variant of the situation with
$\mathbb N$, which half the world (the mistaken half!) considers to include
zero. – Mariano Suárez-Álvarez♦ Aug 6 '10 at 9:05
8

It is

Source: math.stackexchange.com/questions/1706/does-set-mathbbr-include-zero

## Positive real numbers - Wikipedia

--------------------

** Positive real numbers **

In mathematics, the set of *positive real numbers*,
R>={x∈R∣x>}{\displaystyle \mathbb {R} _{>0}=\left\{x\in \mathbb {R}
\mid x>0\right\}}\mathbb{R}_{>0} = \left\{ x \in \mathbb{R} \mid x > 0
\right\}, is the subset of those real numbers that are greater than zero.

In a complex plane, R>{\displaystyle \mathbb {R} _{>0}}{\mathbb {R}}_{{>0}}
is identified with the *positive real axis* and is usually drawn as a
horizontal ray. This ray is used as reference in the polar form of a
complex number. The real positive axis corresponds to complex numbers
z=|z|eiφ{\displaystyle z=|z|\mathrm {e} ^{\mathrm {i} \varphi }}z = |z|
\mathrm{e}^{\mathrm{i}\varphi} with argument φ={\displaystyle \varphi
=0}\varphi = 0.

*Contents*

· 1 Notation
· 2 Properties
· 3 Logarithmic measure
· 5 References

*Notation*

Alternative to R>{\displaystyle \mathbb {R} _{>0}}{\mathbb {R}}_{{>0}}, the
non-standard symbols R+{\displaystyle \mathbb {R} _{+}}\mathbb {R} _{+} and
R+{\displaystyle \mathbb {R} ^{+}}{\mathbb {R}}^{{+}} are often used.
However, this may lead to confusion, as some authors use them to denote the
set of *non-negative real numbers*, R≥={x∈R∣x≥}{\displaystyle
\mathbb {R} _{\geq 0}=\left\{x\in \mathbb {R} \mid x\geq
0\right\}}\mathbb{R}_{\geq 0} = \left\{ x \in \mathbb{R} \mid x \geq 0
\right\}, which explicitly includes zero. The non-negative reals serve as
the range for metrics, norms, and measures in mathematics.

*Properties*

The set R>{\displaystyle \mathbb {R} _{>0}}{\mathbb {R}}_{{>0}} is closed
under addition, multiplication, and division. It inherits a topology from
the real line and, thus, has the structure of a multiplicative topological
group or of an additive topological semigroup.

For a given positive real number /x/, the sequence {/x/^/n/} of its
integral powers has three different fates: When /x/ â (0, 1) the limit
is zero and when /x/ â (1, â) the limit is infinity, while

Source: en.wikipedia.org/wiki/Positive_real_numbers