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


-current community -

· blog chat
· Mathematics Meta

- your communities -

Sign up or log in to customize your list.

-more stack exchange communities -

company blog
Stack Exchange Inbox Reputation and Badges
sign up log in tour help

· Tour Start here for a quick overview of the site
· Help Center Detailed answers to any questions you might have
· Meta Discuss the workings and policies of this site
· About Us Learn more about Stack Overflow the company
· Business Learn more about hiring developers or posting ads with us


· Questions
· Tags
· Users
· Badges
· Unanswered

· Ask Question

Mathematics Stack Exchange is a question and answer site for people
studying math at any level and professionals in related fields. Join them;
it only takes a minute:

Sign up
*Here's how it works:*

1. Anybody can ask a question
2. Anybody can answer
3. The best answers are voted up and rise to the top

** 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


© 2005-2018