Can $mathbb R$ be written as $(-infty , infty)$?
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I was thinking about if $mathbb R$ could be written as $(-infty , infty)$. I'm not sure if it's okay, because I've read somewhere (I can't remember where) that $(-infty , infty)$ declares extended real line, which is totally different from $mathbb R$.
soft-question notation real-numbers infinity
edited Aug 12 at 8:04
Adrian
5,1991035
asked Aug 12 at 7:59
Anik Bhowmick
430317
 |Â
show 1 more comment
up vote
3
down vote
favorite
1
I was thinking about if $mathbb R$ could be written as $(-infty , infty)$. I'm not sure if it's okay, because I've read somewhere (I can't remember where) that $(-infty , infty)$ declares extended real line, which is totally different from $mathbb R$.
soft-question notation real-numbers infinity
edited Aug 12 at 8:04
Adrian
5,1991035
asked Aug 12 at 7:59
Anik Bhowmick
430317
3
Where you read that are more probably write...but it is a matter of agreement. Better, write $;Bbb R=(-infty,,infty);$ . I don't think anyone dealing with mathematics will misunderstand that.
– DonAntonio
Aug 12 at 8:01
Is it okay to write ??@DonAntonio
– Anik Bhowmick
Aug 12 at 8:02
1
You can write it, its just more work and more to read.
– copper.hat
Aug 12 at 8:04
@AnikBhowmick I was going through your profile and found that you haven't accepted any answers to the questions you've asked so far. Consider accepting an answer if it resolves your question, by clicking on the tick mark below the upvote/downvote buttons.
– Brahadeesh
Aug 12 at 8:26
Thanks @Brahadeesh, I really didn't know how to accept answers.
– Anik Bhowmick
Aug 12 at 8:35
 |Â
show 1 more comment
up vote
3
down vote
favorite
1
up vote
3
down vote
favorite
1
1
I was thinking about if $mathbb R$ could be written as $(-infty , infty)$. I'm not sure if it's okay, because I've read somewhere (I can't remember where) that $(-infty , infty)$ declares extended real line, which is totally different from $mathbb R$.
soft-question notation real-numbers infinity
edited Aug 12 at 8:04
Adrian
5,1991035
asked Aug 12 at 7:59
Anik Bhowmick
430317
I was thinking about if $mathbb R$ could be written as $(-infty , infty)$. I'm not sure if it's okay, because I've read somewhere (I can't remember where) that $(-infty , infty)$ declares extended real line, which is totally different from $mathbb R$.
soft-question notation real-numbers infinity
edited Aug 12 at 8:04
Adrian
5,1991035
asked Aug 12 at 7:59
Anik Bhowmick
430317
edited Aug 12 at 8:04
Adrian
5,1991035
edited Aug 12 at 8:04
Adrian
5,1991035
edited Aug 12 at 8:04
Adrian
5,1991035
5,1991035
asked Aug 12 at 7:59
Anik Bhowmick
430317
asked Aug 12 at 7:59
Anik Bhowmick
430317
asked Aug 12 at 7:59
Anik Bhowmick
430317
430317
3
Where you read that are more probably write...but it is a matter of agreement. Better, write $;Bbb R=(-infty,,infty);$ . I don't think anyone dealing with mathematics will misunderstand that.
– DonAntonio
Aug 12 at 8:01
Is it okay to write ??@DonAntonio
– Anik Bhowmick
Aug 12 at 8:02
1
You can write it, its just more work and more to read.
– copper.hat
Aug 12 at 8:04
@AnikBhowmick I was going through your profile and found that you haven't accepted any answers to the questions you've asked so far. Consider accepting an answer if it resolves your question, by clicking on the tick mark below the upvote/downvote buttons.
– Brahadeesh
Aug 12 at 8:26
Thanks @Brahadeesh, I really didn't know how to accept answers.
– Anik Bhowmick
Aug 12 at 8:35
 |Â
show 1 more comment
3
Where you read that are more probably write...but it is a matter of agreement. Better, write $;Bbb R=(-infty,,infty);$ . I don't think anyone dealing with mathematics will misunderstand that.
– DonAntonio
Aug 12 at 8:01
Is it okay to write ??@DonAntonio
– Anik Bhowmick
Aug 12 at 8:02
1
You can write it, its just more work and more to read.
– copper.hat
Aug 12 at 8:04
@AnikBhowmick I was going through your profile and found that you haven't accepted any answers to the questions you've asked so far. Consider accepting an answer if it resolves your question, by clicking on the tick mark below the upvote/downvote buttons.
– Brahadeesh
Aug 12 at 8:26
Thanks @Brahadeesh, I really didn't know how to accept answers.
– Anik Bhowmick
Aug 12 at 8:35
3
3
Where you read that are more probably write...but it is a matter of agreement. Better, write $;Bbb R=(-infty,,infty);$ . I don't think anyone dealing with mathematics will misunderstand that.
– DonAntonio
Aug 12 at 8:01
Where you read that are more probably write...but it is a matter of agreement. Better, write $;Bbb R=(-infty,,infty);$ . I don't think anyone dealing with mathematics will misunderstand that.
– DonAntonio
Aug 12 at 8:01
Is it okay to write ??@DonAntonio
– Anik Bhowmick
Aug 12 at 8:02
Is it okay to write ??@DonAntonio
– Anik Bhowmick
Aug 12 at 8:02
1
1
You can write it, its just more work and more to read.
– copper.hat
Aug 12 at 8:04
You can write it, its just more work and more to read.
– copper.hat
Aug 12 at 8:04
@AnikBhowmick I was going through your profile and found that you haven't accepted any answers to the questions you've asked so far. Consider accepting an answer if it resolves your question, by clicking on the tick mark below the upvote/downvote buttons.
– Brahadeesh
Aug 12 at 8:26
@AnikBhowmick I was going through your profile and found that you haven't accepted any answers to the questions you've asked so far. Consider accepting an answer if it resolves your question, by clicking on the tick mark below the upvote/downvote buttons.
– Brahadeesh
Aug 12 at 8:26
Thanks @Brahadeesh, I really didn't know how to accept answers.
– Anik Bhowmick
Aug 12 at 8:35
Thanks @Brahadeesh, I really didn't know how to accept answers.
– Anik Bhowmick
Aug 12 at 8:35
 |Â
show 1 more comment
2 Answers
2
active
oldest
votes
up vote
4
down vote
accepted
Yes. Although it's unusual, it makes sense to write $mathbb R$ as $(-infty,infty)$. That would never be the extended real line, which would be denoted by $[-infty,infty]$.
answered Aug 12 at 8:02
José Carlos Santos
116k1699178
But can $infty$ be included in closed brackets ?? I mean, $infty$ is not a number, how can it be an element of a set ??
– Anik Bhowmick
Aug 12 at 8:04
In extended real line, $infty$ is a number (though it's not a real number).
– user529760
Aug 12 at 8:06
And $emptyset$ is not a number either, but we write $emptyset$, don't we? Besides, we are talking about the extended real line here, right?! Therefore, it is supposed to contain something else besides the real numbers.
– José Carlos Santos
Aug 12 at 8:06
@JoséCarlosSantos: $emptyset$ is really another case. That is the set containing the empty set, we can have sets of anything.
– Henrik
Aug 12 at 8:29
1
@AnikBhowmick I'm glad I could help.
– José Carlos Santos
Aug 12 at 11:31
 |Â
show 1 more comment
up vote
2
down vote
It can be written that way, it doesn't mean it should be.
Have you ever heard of "complex infinity" or "directionless infinity"? Your readers would quickly realize you're not referring to either of those, but it could still be enough to cause a little cognitive dissonance and disrupt the flow of your presentation.
If you don't like $mathbb R$ for whatever reason, you can always use $textbf R$ instead. You don't lose any clarity that way.
answered Aug 12 at 21:41
Robert Soupe
10.1k21947
What's the difference between the two $R$'s?
– goblin
Aug 12 at 22:30
@goblin Is this one of those you already know but you're checking if I know?
– Robert Soupe
Aug 13 at 0:53
No I haven't heard any of them. And besides of that, what does $R$ denote ??
– Anik Bhowmick
Aug 13 at 1:48
2
$mathbb R$ is blackboard bold for the set of reals, $textbf R$ is for the set of reals for people who think blackboard bold is for the blackboard only, and $R$ can mean whatever you want it to mean just as long as you say what that is.
– Robert Soupe
Aug 13 at 3:22
1
@RobertSoupe, fair enough. I thought maybe you were proposing that $mathbfR$ be used for the affinely extended real line, or perhaps the projectively extended one.
– goblin
Aug 13 at 8:53
 |Â
show 1 more comment
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
accepted
Yes. Although it's unusual, it makes sense to write $mathbb R$ as $(-infty,infty)$. That would never be the extended real line, which would be denoted by $[-infty,infty]$.
answered Aug 12 at 8:02
José Carlos Santos
116k1699178
But can $infty$ be included in closed brackets ?? I mean, $infty$ is not a number, how can it be an element of a set ??
– Anik Bhowmick
Aug 12 at 8:04
In extended real line, $infty$ is a number (though it's not a real number).
– user529760
Aug 12 at 8:06
And $emptyset$ is not a number either, but we write $emptyset$, don't we? Besides, we are talking about the extended real line here, right?! Therefore, it is supposed to contain something else besides the real numbers.
– José Carlos Santos
Aug 12 at 8:06
@JoséCarlosSantos: $emptyset$ is really another case. That is the set containing the empty set, we can have sets of anything.
– Henrik
Aug 12 at 8:29
1
@AnikBhowmick I'm glad I could help.
– José Carlos Santos
Aug 12 at 11:31
 |Â
show 1 more comment
up vote
4
down vote
accepted
Yes. Although it's unusual, it makes sense to write $mathbb R$ as $(-infty,infty)$. That would never be the extended real line, which would be denoted by $[-infty,infty]$.
answered Aug 12 at 8:02
José Carlos Santos
116k1699178
But can $infty$ be included in closed brackets ?? I mean, $infty$ is not a number, how can it be an element of a set ??
– Anik Bhowmick
Aug 12 at 8:04
In extended real line, $infty$ is a number (though it's not a real number).
– user529760
Aug 12 at 8:06
And $emptyset$ is not a number either, but we write $emptyset$, don't we? Besides, we are talking about the extended real line here, right?! Therefore, it is supposed to contain something else besides the real numbers.
– José Carlos Santos
Aug 12 at 8:06
@JoséCarlosSantos: $emptyset$ is really another case. That is the set containing the empty set, we can have sets of anything.
– Henrik
Aug 12 at 8:29
1
@AnikBhowmick I'm glad I could help.
– José Carlos Santos
Aug 12 at 11:31
 |Â
show 1 more comment
up vote
4
down vote
accepted
up vote
4
down vote
accepted
Yes. Although it's unusual, it makes sense to write $mathbb R$ as $(-infty,infty)$. That would never be the extended real line, which would be denoted by $[-infty,infty]$.
answered Aug 12 at 8:02
José Carlos Santos
116k1699178
Yes. Although it's unusual, it makes sense to write $mathbb R$ as $(-infty,infty)$. That would never be the extended real line, which would be denoted by $[-infty,infty]$.
answered Aug 12 at 8:02
José Carlos Santos
116k1699178
answered Aug 12 at 8:02
José Carlos Santos
116k1699178
answered Aug 12 at 8:02
José Carlos Santos
116k1699178
answered Aug 12 at 8:02
José Carlos Santos
116k1699178
116k1699178
But can $infty$ be included in closed brackets ?? I mean, $infty$ is not a number, how can it be an element of a set ??
– Anik Bhowmick
Aug 12 at 8:04
In extended real line, $infty$ is a number (though it's not a real number).
– user529760
Aug 12 at 8:06
And $emptyset$ is not a number either, but we write $emptyset$, don't we? Besides, we are talking about the extended real line here, right?! Therefore, it is supposed to contain something else besides the real numbers.
– José Carlos Santos
Aug 12 at 8:06
@JoséCarlosSantos: $emptyset$ is really another case. That is the set containing the empty set, we can have sets of anything.
– Henrik
Aug 12 at 8:29
1
@AnikBhowmick I'm glad I could help.
– José Carlos Santos
Aug 12 at 11:31
 |Â
show 1 more comment
But can $infty$ be included in closed brackets ?? I mean, $infty$ is not a number, how can it be an element of a set ??
– Anik Bhowmick
Aug 12 at 8:04
In extended real line, $infty$ is a number (though it's not a real number).
– user529760
Aug 12 at 8:06
And $emptyset$ is not a number either, but we write $emptyset$, don't we? Besides, we are talking about the extended real line here, right?! Therefore, it is supposed to contain something else besides the real numbers.
– José Carlos Santos
Aug 12 at 8:06
@JoséCarlosSantos: $emptyset$ is really another case. That is the set containing the empty set, we can have sets of anything.
– Henrik
Aug 12 at 8:29
1
@AnikBhowmick I'm glad I could help.
– José Carlos Santos
Aug 12 at 11:31
But can $infty$ be included in closed brackets ?? I mean, $infty$ is not a number, how can it be an element of a set ??
– Anik Bhowmick
Aug 12 at 8:04
But can $infty$ be included in closed brackets ?? I mean, $infty$ is not a number, how can it be an element of a set ??
– Anik Bhowmick
Aug 12 at 8:04
In extended real line, $infty$ is a number (though it's not a real number).
– user529760
Aug 12 at 8:06
In extended real line, $infty$ is a number (though it's not a real number).
– user529760
Aug 12 at 8:06
And $emptyset$ is not a number either, but we write $emptyset$, don't we? Besides, we are talking about the extended real line here, right?! Therefore, it is supposed to contain something else besides the real numbers.
– José Carlos Santos
Aug 12 at 8:06
And $emptyset$ is not a number either, but we write $emptyset$, don't we? Besides, we are talking about the extended real line here, right?! Therefore, it is supposed to contain something else besides the real numbers.
– José Carlos Santos
Aug 12 at 8:06
@JoséCarlosSantos: $emptyset$ is really another case. That is the set containing the empty set, we can have sets of anything.
– Henrik
Aug 12 at 8:29
@JoséCarlosSantos: $emptyset$ is really another case. That is the set containing the empty set, we can have sets of anything.
– Henrik
Aug 12 at 8:29
1
1
@AnikBhowmick I'm glad I could help.
– José Carlos Santos
Aug 12 at 11:31
@AnikBhowmick I'm glad I could help.
– José Carlos Santos
Aug 12 at 11:31
 |Â
show 1 more comment
up vote
2
down vote
It can be written that way, it doesn't mean it should be.
Have you ever heard of "complex infinity" or "directionless infinity"? Your readers would quickly realize you're not referring to either of those, but it could still be enough to cause a little cognitive dissonance and disrupt the flow of your presentation.
If you don't like $mathbb R$ for whatever reason, you can always use $textbf R$ instead. You don't lose any clarity that way.
answered Aug 12 at 21:41
Robert Soupe
10.1k21947
What's the difference between the two $R$'s?
– goblin
Aug 12 at 22:30
@goblin Is this one of those you already know but you're checking if I know?
– Robert Soupe
Aug 13 at 0:53
No I haven't heard any of them. And besides of that, what does $R$ denote ??
– Anik Bhowmick
Aug 13 at 1:48
2
$mathbb R$ is blackboard bold for the set of reals, $textbf R$ is for the set of reals for people who think blackboard bold is for the blackboard only, and $R$ can mean whatever you want it to mean just as long as you say what that is.
– Robert Soupe
Aug 13 at 3:22
1
@RobertSoupe, fair enough. I thought maybe you were proposing that $mathbfR$ be used for the affinely extended real line, or perhaps the projectively extended one.
– goblin
Aug 13 at 8:53
 |Â
show 1 more comment
up vote
2
down vote
It can be written that way, it doesn't mean it should be.
Have you ever heard of "complex infinity" or "directionless infinity"? Your readers would quickly realize you're not referring to either of those, but it could still be enough to cause a little cognitive dissonance and disrupt the flow of your presentation.
If you don't like $mathbb R$ for whatever reason, you can always use $textbf R$ instead. You don't lose any clarity that way.
answered Aug 12 at 21:41
Robert Soupe
10.1k21947
What's the difference between the two $R$'s?
– goblin
Aug 12 at 22:30
@goblin Is this one of those you already know but you're checking if I know?
– Robert Soupe
Aug 13 at 0:53
No I haven't heard any of them. And besides of that, what does $R$ denote ??
– Anik Bhowmick
Aug 13 at 1:48
2
$mathbb R$ is blackboard bold for the set of reals, $textbf R$ is for the set of reals for people who think blackboard bold is for the blackboard only, and $R$ can mean whatever you want it to mean just as long as you say what that is.
– Robert Soupe
Aug 13 at 3:22
1
@RobertSoupe, fair enough. I thought maybe you were proposing that $mathbfR$ be used for the affinely extended real line, or perhaps the projectively extended one.
– goblin
Aug 13 at 8:53
 |Â
show 1 more comment
up vote
2
down vote
up vote
2
down vote
It can be written that way, it doesn't mean it should be.
Have you ever heard of "complex infinity" or "directionless infinity"? Your readers would quickly realize you're not referring to either of those, but it could still be enough to cause a little cognitive dissonance and disrupt the flow of your presentation.
If you don't like $mathbb R$ for whatever reason, you can always use $textbf R$ instead. You don't lose any clarity that way.
answered Aug 12 at 21:41
Robert Soupe
10.1k21947
It can be written that way, it doesn't mean it should be.
Have you ever heard of "complex infinity" or "directionless infinity"? Your readers would quickly realize you're not referring to either of those, but it could still be enough to cause a little cognitive dissonance and disrupt the flow of your presentation.
If you don't like $mathbb R$ for whatever reason, you can always use $textbf R$ instead. You don't lose any clarity that way.
answered Aug 12 at 21:41
Robert Soupe
10.1k21947
answered Aug 12 at 21:41
Robert Soupe
10.1k21947
answered Aug 12 at 21:41
Robert Soupe
10.1k21947
answered Aug 12 at 21:41
Robert Soupe
10.1k21947
10.1k21947
What's the difference between the two $R$'s?
– goblin
Aug 12 at 22:30
@goblin Is this one of those you already know but you're checking if I know?
– Robert Soupe
Aug 13 at 0:53
No I haven't heard any of them. And besides of that, what does $R$ denote ??
– Anik Bhowmick
Aug 13 at 1:48
2
$mathbb R$ is blackboard bold for the set of reals, $textbf R$ is for the set of reals for people who think blackboard bold is for the blackboard only, and $R$ can mean whatever you want it to mean just as long as you say what that is.
– Robert Soupe
Aug 13 at 3:22
1
@RobertSoupe, fair enough. I thought maybe you were proposing that $mathbfR$ be used for the affinely extended real line, or perhaps the projectively extended one.
– goblin
Aug 13 at 8:53
 |Â
show 1 more comment
What's the difference between the two $R$'s?
– goblin
Aug 12 at 22:30
@goblin Is this one of those you already know but you're checking if I know?
– Robert Soupe
Aug 13 at 0:53
No I haven't heard any of them. And besides of that, what does $R$ denote ??
– Anik Bhowmick
Aug 13 at 1:48
2
$mathbb R$ is blackboard bold for the set of reals, $textbf R$ is for the set of reals for people who think blackboard bold is for the blackboard only, and $R$ can mean whatever you want it to mean just as long as you say what that is.
– Robert Soupe
Aug 13 at 3:22
1
@RobertSoupe, fair enough. I thought maybe you were proposing that $mathbfR$ be used for the affinely extended real line, or perhaps the projectively extended one.
– goblin
Aug 13 at 8:53
What's the difference between the two $R$'s?
– goblin
Aug 12 at 22:30
What's the difference between the two $R$'s?
– goblin
Aug 12 at 22:30
@goblin Is this one of those you already know but you're checking if I know?
– Robert Soupe
Aug 13 at 0:53
@goblin Is this one of those you already know but you're checking if I know?
– Robert Soupe
Aug 13 at 0:53
No I haven't heard any of them. And besides of that, what does $R$ denote ??
– Anik Bhowmick
Aug 13 at 1:48
No I haven't heard any of them. And besides of that, what does $R$ denote ??
– Anik Bhowmick
Aug 13 at 1:48
2
2
$mathbb R$ is blackboard bold for the set of reals, $textbf R$ is for the set of reals for people who think blackboard bold is for the blackboard only, and $R$ can mean whatever you want it to mean just as long as you say what that is.
– Robert Soupe
Aug 13 at 3:22
$mathbb R$ is blackboard bold for the set of reals, $textbf R$ is for the set of reals for people who think blackboard bold is for the blackboard only, and $R$ can mean whatever you want it to mean just as long as you say what that is.
– Robert Soupe
Aug 13 at 3:22
1
1
@RobertSoupe, fair enough. I thought maybe you were proposing that $mathbfR$ be used for the affinely extended real line, or perhaps the projectively extended one.
– goblin
Aug 13 at 8:53
@RobertSoupe, fair enough. I thought maybe you were proposing that $mathbfR$ be used for the affinely extended real line, or perhaps the projectively extended one.
– goblin
Aug 13 at 8:53
 |Â
show 1 more comment
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3
Where you read that are more probably write...but it is a matter of agreement. Better, write $;Bbb R=(-infty,,infty);$ . I don't think anyone dealing with mathematics will misunderstand that.
– DonAntonio
Aug 12 at 8:01
Is it okay to write ??@DonAntonio
– Anik Bhowmick
Aug 12 at 8:02
1
You can write it, its just more work and more to read.
– copper.hat
Aug 12 at 8:04
@AnikBhowmick I was going through your profile and found that you haven't accepted any answers to the questions you've asked so far. Consider accepting an answer if it resolves your question, by clicking on the tick mark below the upvote/downvote buttons.
– Brahadeesh
Aug 12 at 8:26
Thanks @Brahadeesh, I really didn't know how to accept answers.
– Anik Bhowmick
Aug 12 at 8:35