Mixing
The meaning of $Bbb R^Bbb N$ [duplicate]
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
This question already has an answer here:
Meaning of a set in the exponent
2 answers
I know that $Bbb R$ is the real line, that $Bbb R^Bbb 2$is some pair of numbers of numbers from the real line and that $Bbb R^3$ is a triplet of numbers from the real line etc.. So I assume that $Bbb R^Bbb N $is an infinite selection of numbers from the real line , is that correct ? if so what specifically does it mean to say $B=a in Bbb R ^Bbb N $ ?
general-topology notation
asked Jul 31 at 5:13
exodius
717215
marked as duplicate by Asaf Karagila general-topology
Users with the  general-topology badge can single-handedly close general-topology questions as duplicates and reopen them as needed.
StackExchange.ready(function()
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function()
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function()
$hover.showInfoMessage('',
messageElement: $msg.clone().show(),
transient: false,
position: my: 'bottom left', at: 'top center', offsetTop: -7 ,
dismissable: false,
relativeToBody: true
);
,
function()
StackExchange.helpers.removeMessages();
);
);
);
Jul 31 at 7:41
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |Â
up vote
0
down vote
favorite
This question already has an answer here:
Meaning of a set in the exponent
2 answers
I know that $Bbb R$ is the real line, that $Bbb R^Bbb 2$is some pair of numbers of numbers from the real line and that $Bbb R^3$ is a triplet of numbers from the real line etc.. So I assume that $Bbb R^Bbb N $is an infinite selection of numbers from the real line , is that correct ? if so what specifically does it mean to say $B=a in Bbb R ^Bbb N $ ?
general-topology notation
asked Jul 31 at 5:13
exodius
717215
marked as duplicate by Asaf Karagila general-topology
Users with the  general-topology badge can single-handedly close general-topology questions as duplicates and reopen them as needed.
StackExchange.ready(function()
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function()
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function()
$hover.showInfoMessage('',
messageElement: $msg.clone().show(),
transient: false,
position: my: 'bottom left', at: 'top center', offsetTop: -7 ,
dismissable: false,
relativeToBody: true
);
,
function()
StackExchange.helpers.removeMessages();
);
);
);
Jul 31 at 7:41
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
1
It is the collection of functions $mathbbN to mathbbR$, that is, the real sequences. In general, $A^B$ is the collection of functions $B to A$. Think of $B$ as the index set.
– copper.hat
Jul 31 at 5:16
No, $mathbb R$ is not "some pair of numbers", it is the set of all pairs of real numbers. $(sqrt2,pi)$ is some pair of real numbers, but $(sqrt2,pi)nemathbb R.$
– bof
Jul 31 at 5:31
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
This question already has an answer here:
Meaning of a set in the exponent
2 answers
I know that $Bbb R$ is the real line, that $Bbb R^Bbb 2$is some pair of numbers of numbers from the real line and that $Bbb R^3$ is a triplet of numbers from the real line etc.. So I assume that $Bbb R^Bbb N $is an infinite selection of numbers from the real line , is that correct ? if so what specifically does it mean to say $B=a in Bbb R ^Bbb N $ ?
general-topology notation
asked Jul 31 at 5:13
exodius
717215
This question already has an answer here:
Meaning of a set in the exponent
2 answers
I know that $Bbb R$ is the real line, that $Bbb R^Bbb 2$is some pair of numbers of numbers from the real line and that $Bbb R^3$ is a triplet of numbers from the real line etc.. So I assume that $Bbb R^Bbb N $is an infinite selection of numbers from the real line , is that correct ? if so what specifically does it mean to say $B=a in Bbb R ^Bbb N $ ?
This question already has an answer here:
Meaning of a set in the exponent
2 answers
general-topology notation
asked Jul 31 at 5:13
exodius
717215
asked Jul 31 at 5:13
exodius
717215
asked Jul 31 at 5:13
exodius
717215
asked Jul 31 at 5:13
exodius
717215
717215
marked as duplicate by Asaf Karagila general-topology
Users with the  general-topology badge can single-handedly close general-topology questions as duplicates and reopen them as needed.
StackExchange.ready(function()
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function()
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function()
$hover.showInfoMessage('',
messageElement: $msg.clone().show(),
transient: false,
position: my: 'bottom left', at: 'top center', offsetTop: -7 ,
dismissable: false,
relativeToBody: true
);
,
function()
StackExchange.helpers.removeMessages();
);
);
);
Jul 31 at 7:41
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Asaf Karagila general-topology
Users with the  general-topology badge can single-handedly close general-topology questions as duplicates and reopen them as needed.
StackExchange.ready(function()
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function()
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function()
$hover.showInfoMessage('',
messageElement: $msg.clone().show(),
transient: false,
position: my: 'bottom left', at: 'top center', offsetTop: -7 ,
dismissable: false,
relativeToBody: true
);
,
function()
StackExchange.helpers.removeMessages();
);
);
);
Jul 31 at 7:41
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
1
It is the collection of functions $mathbbN to mathbbR$, that is, the real sequences. In general, $A^B$ is the collection of functions $B to A$. Think of $B$ as the index set.
– copper.hat
Jul 31 at 5:16
No, $mathbb R$ is not "some pair of numbers", it is the set of all pairs of real numbers. $(sqrt2,pi)$ is some pair of real numbers, but $(sqrt2,pi)nemathbb R.$
– bof
Jul 31 at 5:31
add a comment |Â
1
It is the collection of functions $mathbbN to mathbbR$, that is, the real sequences. In general, $A^B$ is the collection of functions $B to A$. Think of $B$ as the index set.
– copper.hat
Jul 31 at 5:16
No, $mathbb R$ is not "some pair of numbers", it is the set of all pairs of real numbers. $(sqrt2,pi)$ is some pair of real numbers, but $(sqrt2,pi)nemathbb R.$
– bof
Jul 31 at 5:31
1
1
It is the collection of functions $mathbbN to mathbbR$, that is, the real sequences. In general, $A^B$ is the collection of functions $B to A$. Think of $B$ as the index set.
– copper.hat
Jul 31 at 5:16
It is the collection of functions $mathbbN to mathbbR$, that is, the real sequences. In general, $A^B$ is the collection of functions $B to A$. Think of $B$ as the index set.
– copper.hat
Jul 31 at 5:16
No, $mathbb R$ is not "some pair of numbers", it is the set of all pairs of real numbers. $(sqrt2,pi)$ is some pair of real numbers, but $(sqrt2,pi)nemathbb R.$
– bof
Jul 31 at 5:31
No, $mathbb R$ is not "some pair of numbers", it is the set of all pairs of real numbers. $(sqrt2,pi)$ is some pair of real numbers, but $(sqrt2,pi)nemathbb R.$
– bof
Jul 31 at 5:31
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
Precisely speaking, $mathbbR^mathbbN$ is the set of real sequence. It is not even an infinite selection of real numbers, but a COUNTABLE selection of real numbers.
answered Jul 31 at 5:18
Jerry
374211
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Precisely speaking, $mathbbR^mathbbN$ is the set of real sequence. It is not even an infinite selection of real numbers, but a COUNTABLE selection of real numbers.
answered Jul 31 at 5:18
Jerry
374211
add a comment |Â
up vote
1
down vote
Precisely speaking, $mathbbR^mathbbN$ is the set of real sequence. It is not even an infinite selection of real numbers, but a COUNTABLE selection of real numbers.
answered Jul 31 at 5:18
Jerry
374211
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Precisely speaking, $mathbbR^mathbbN$ is the set of real sequence. It is not even an infinite selection of real numbers, but a COUNTABLE selection of real numbers.
answered Jul 31 at 5:18
Jerry
374211
Precisely speaking, $mathbbR^mathbbN$ is the set of real sequence. It is not even an infinite selection of real numbers, but a COUNTABLE selection of real numbers.
answered Jul 31 at 5:18
Jerry
374211
answered Jul 31 at 5:18
Jerry
374211
answered Jul 31 at 5:18
Jerry
374211
answered Jul 31 at 5:18
Jerry
374211
374211
add a comment |Â
add a comment |Â
1
It is the collection of functions $mathbbN to mathbbR$, that is, the real sequences. In general, $A^B$ is the collection of functions $B to A$. Think of $B$ as the index set.
– copper.hat
Jul 31 at 5:16
No, $mathbb R$ is not "some pair of numbers", it is the set of all pairs of real numbers. $(sqrt2,pi)$ is some pair of real numbers, but $(sqrt2,pi)nemathbb R.$
– bof
Jul 31 at 5:31