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

up vote 9 down vote favorite
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 $\mathbf ℝ^+$ is.

notation number-systems

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


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

It is


does r plus include zero

Positive real numbers - Wikipedia


** Positive real numbers **

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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.


· 1 Notation
· 2 Properties
· 3 Logarithmic measure
· 4 See also
· 5 References


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.


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/ ∈ (0, 1) the limit
is zero and when /x/ ∈ (1, ∞) the limit is infinity, while


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