What is the meaning of the superscript "+"?

[Buzz Bloom]

In the problem statement for problem (10b) in the thread

https://www.physicsforums.com/threads/math-challenge-november-2018.960003/​

the following notation is used:
What is the meaning of the superscript "+"?

 

[fresh_42]

In the problem statement for problem (10b) in the thread

https://www.physicsforums.com/threads/math-challenge-november-2018.960003/​

the following notation is used:
What is the meaning of the superscript "+"?View attachment 234346

I haven't found the situation where it has been used, but very likely it means $\mathbb{R}^+=\{\,r\in \mathbb{R}\,|\,r>0\,\}$. In group theory it could also mean the additive group of the real numbers. However, I would rather write the additive group as $(\mathbb{R},+)$.

 

[member 587159]

$\mathbb{R}^+ := \{r \in \mathbb{R}\mid r \geq 0\}$

This is standard notation in my country.

In case you would also encounter the following notation, you'll know what it means: $\mathbb{R}^+_0 := \{r \in \mathbb{R}\mid r > 0\}$

 

[fresh_42]

$\mathbb{R}^+ := \{r \in \mathbb{R}\mid r \geq 0\}$

This is standard notation in my country.

In case you would also encounter the following notation, you'll know what it means: $\mathbb{R}^+_0 := \{r \in \mathbb{R}\mid r > 0\}$

I know it the other way around, which I think makes more sense: $\mathbb{R}^+$ for strictly positive reals and $\mathbb{R}_0^+$ if zero is included. Your notation is strange: you positively (include) write + but negatively (exclude) 0. Very strange. I have never seen this before.

Other notations are: $\mathbb{R}^+=\mathbb{R}_{>0}\; , \;\mathbb{R}^+_0=\mathbb{R}_{\geq 0}\; , \;\mathbb{R}^\times = \mathbb{R}-\{\,0\,\}$.

 

[member 587159]

I know it the other way around, which I think makes more sense: $\mathbb{R}^+$ for strictly positive reals and $\mathbb{R}_0^+$ if zero is included. Your notation is strange: you positively (include) write + but negatively (exclude) 0. Very strange. I have never seen this before.

Other notations are: $\mathbb{R}^+=\mathbb{R}_{>0}\; , \;\mathbb{R}^+_0=\mathbb{R}_{\geq 0}\; , \;\mathbb{R}^\times = \mathbb{R}-\{\,0\,\}$.

Interesting how things can vary depending on the country!

 

[Mark44]

$\mathbb{R}^+ := \{r \in \mathbb{R}\mid r \geq 0\}$

This is standard notation in my country.

In case you would also encounter the following notation, you'll know what it means: $\mathbb{R}^+_0 := \{r \in \mathbb{R}\mid r > 0\}$

It makes more sense the other way around as you have them.
IOW, this makes more sense:
$\mathbb{R}^+ := \{r \in \mathbb{R}\mid r \gt 0\}$
and $\mathbb{R}^+_0 := \{r \in \mathbb{R}\mid r \ge 0\}$
I must admit that I've never encountered the latter notation.

 

[member 587159]

It makes more sense the other way around as you have them.
IOW, this makes more sense:
$\mathbb{R}^+ := \{r \in \mathbb{R}\mid r \gt 0\}$
and $\mathbb{R}^+_0 := \{r \in \mathbb{R}\mid r \ge 0\}$
I must admit that I've never encountered the latter notation.

Wikipedia says both notations are possible, but nevertheless it is worth mentioning what certain notation mean.

https://en.m.wikipedia.org/wiki/Positive_real_numbers

 

[Buzz Bloom]

Hi @Math QED:

Thanks for the Wikipedia citation. I did make an effort to find an explanation in Wikipedia, but I did not use a search phrase that found anything useful.

Regards,
Buzz

 

[Mark44]

Wikipedia says both notations are possible, but nevertheless it is worth mentioning what certain notation mean.

https://en.m.wikipedia.org/wiki/Positive_real_numbers

I don't see this notation -- $\mathbb{R}^+_0$ -- anywhere on the page you cited.

 

[member 587159]

I don't see this notation -- $\mathbb{R}^+_0$ -- anywhere on the page you cited.

The page shows $\mathbb{R}^+$ for 0 included though. No need to discuss trivialities like this though.

 

[Mark44]

The page shows $\mathbb{R}^+$ for 0 included though. No need to discuss trivialities like this though.

My response was to what you wrote at the bottom of post #3:

In case you would also encounter the following notation, you'll know what it means: $\mathbb{R}^+_0 := \{r \in \mathbb{R}\mid r > 0\}$

Trivial or not, it's not listed in the wiki article you cited.