Notation in point set Topology
Clash Royale CLAN TAG#URR8PPP
$begingroup$
In $mathbb R setminus mathbb Q$ and $mathbb R /mathbb Q$, what do these ("$setminus$","$/$") symbols between the sets of real and rational numbers mean?
real-analysis general-topology notation
edited Feb 9 at 22:26
GNUSupporter 8964民主女神 地下教會
14k82650
asked Feb 9 at 17:56
user639820user639820
113
$endgroup$
add a comment |
$begingroup$
In $mathbb R setminus mathbb Q$ and $mathbb R /mathbb Q$, what do these ("$setminus$","$/$") symbols between the sets of real and rational numbers mean?
real-analysis general-topology notation
edited Feb 9 at 22:26
GNUSupporter 8964民主女神 地下教會
14k82650
asked Feb 9 at 17:56
user639820user639820
113
$endgroup$
$begingroup$
Those are both versions of the "set difference", which is used probably determined by whichever notation is simpler to typeset. A/B= AB= the set of all elements of A that are NOT in B.
$endgroup$
– user247327
Feb 9 at 18:02
8
$begingroup$
@user247327 $A/B$ does not denote the set theoretic difference!
$endgroup$
– Alex Kruckman
Feb 9 at 18:20
add a comment |
$begingroup$
In $mathbb R setminus mathbb Q$ and $mathbb R /mathbb Q$, what do these ("$setminus$","$/$") symbols between the sets of real and rational numbers mean?
real-analysis general-topology notation
edited Feb 9 at 22:26
GNUSupporter 8964民主女神 地下教會
14k82650
asked Feb 9 at 17:56
user639820user639820
113
$endgroup$
In $mathbb R setminus mathbb Q$ and $mathbb R /mathbb Q$, what do these ("$setminus$","$/$") symbols between the sets of real and rational numbers mean?
real-analysis general-topology notation
real-analysis general-topology notation
edited Feb 9 at 22:26
GNUSupporter 8964民主女神 地下教會
14k82650
asked Feb 9 at 17:56
user639820user639820
113
edited Feb 9 at 22:26
GNUSupporter 8964民主女神 地下教會
14k82650
asked Feb 9 at 17:56
user639820user639820
113
edited Feb 9 at 22:26
GNUSupporter 8964民主女神 地下教會
14k82650
edited Feb 9 at 22:26
GNUSupporter 8964民主女神 地下教會
14k82650
edited Feb 9 at 22:26
GNUSupporter 8964民主女神 地下教會
14k82650
14k82650
asked Feb 9 at 17:56
user639820user639820
113
asked Feb 9 at 17:56
user639820user639820
113
asked Feb 9 at 17:56
user639820user639820
113
113
$begingroup$
Those are both versions of the "set difference", which is used probably determined by whichever notation is simpler to typeset. A/B= AB= the set of all elements of A that are NOT in B.
$endgroup$
– user247327
Feb 9 at 18:02
8
$begingroup$
@user247327 $A/B$ does not denote the set theoretic difference!
$endgroup$
– Alex Kruckman
Feb 9 at 18:20
add a comment |
$begingroup$
Those are both versions of the "set difference", which is used probably determined by whichever notation is simpler to typeset. A/B= AB= the set of all elements of A that are NOT in B.
$endgroup$
– user247327
Feb 9 at 18:02
8
$begingroup$
@user247327 $A/B$ does not denote the set theoretic difference!
$endgroup$
– Alex Kruckman
Feb 9 at 18:20
$begingroup$
Those are both versions of the "set difference", which is used probably determined by whichever notation is simpler to typeset. A/B= AB= the set of all elements of A that are NOT in B.
$endgroup$
– user247327
Feb 9 at 18:02
$begingroup$
Those are both versions of the "set difference", which is used probably determined by whichever notation is simpler to typeset. A/B= AB= the set of all elements of A that are NOT in B.
$endgroup$
– user247327
Feb 9 at 18:02
8
8
$begingroup$
@user247327 $A/B$ does not denote the set theoretic difference!
$endgroup$
– Alex Kruckman
Feb 9 at 18:20
$begingroup$
@user247327 $A/B$ does not denote the set theoretic difference!
$endgroup$
– Alex Kruckman
Feb 9 at 18:20
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Typically $mathbbRbackslashmathbbQ$ is the set theoretic difference, i.e. the set of all irrationals in this case.
While $mathbbR/mathbbQ$ is the quotient group. It can also mean the result of collapsing a topological subspace to a point. Or the orbit space of $mathbbQ$ acting on $mathbbR$ and potentially other things. So it depends on the context. Either way it is some form of a quotient set.
answered Feb 9 at 18:02
freakishfreakish
12.6k1630
$endgroup$
$begingroup$
Also $mathbbR/mathbbQ$ can denote $mathbbR$ viewed as a field extension of $mathbbQ$.
$endgroup$
– AlephNull
Feb 9 at 22:46
add a comment |
$begingroup$
Depends on the context:
$mathbbR setminus mathbbQ$ is the set difference
between the reals and the rationals, so it equals the set of irrationals.
$mathbbR/mathbbQ$ can mean the quotient of the group of reals by its subgroup of the rationals, (which also gives a topological group) or it can denote a quotient space of the reals where we identify the subset of rationals to a single point.
answered Feb 9 at 18:02
Henno BrandsmaHenno Brandsma
111k348120
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Typically $mathbbRbackslashmathbbQ$ is the set theoretic difference, i.e. the set of all irrationals in this case.
While $mathbbR/mathbbQ$ is the quotient group. It can also mean the result of collapsing a topological subspace to a point. Or the orbit space of $mathbbQ$ acting on $mathbbR$ and potentially other things. So it depends on the context. Either way it is some form of a quotient set.
answered Feb 9 at 18:02
freakishfreakish
12.6k1630
$endgroup$
$begingroup$
Also $mathbbR/mathbbQ$ can denote $mathbbR$ viewed as a field extension of $mathbbQ$.
$endgroup$
– AlephNull
Feb 9 at 22:46
add a comment |
$begingroup$
Typically $mathbbRbackslashmathbbQ$ is the set theoretic difference, i.e. the set of all irrationals in this case.
While $mathbbR/mathbbQ$ is the quotient group. It can also mean the result of collapsing a topological subspace to a point. Or the orbit space of $mathbbQ$ acting on $mathbbR$ and potentially other things. So it depends on the context. Either way it is some form of a quotient set.
answered Feb 9 at 18:02
freakishfreakish
12.6k1630
$endgroup$
$begingroup$
Also $mathbbR/mathbbQ$ can denote $mathbbR$ viewed as a field extension of $mathbbQ$.
$endgroup$
– AlephNull
Feb 9 at 22:46
add a comment |
$begingroup$
Typically $mathbbRbackslashmathbbQ$ is the set theoretic difference, i.e. the set of all irrationals in this case.
While $mathbbR/mathbbQ$ is the quotient group. It can also mean the result of collapsing a topological subspace to a point. Or the orbit space of $mathbbQ$ acting on $mathbbR$ and potentially other things. So it depends on the context. Either way it is some form of a quotient set.
answered Feb 9 at 18:02
freakishfreakish
12.6k1630
$endgroup$
Typically $mathbbRbackslashmathbbQ$ is the set theoretic difference, i.e. the set of all irrationals in this case.
While $mathbbR/mathbbQ$ is the quotient group. It can also mean the result of collapsing a topological subspace to a point. Or the orbit space of $mathbbQ$ acting on $mathbbR$ and potentially other things. So it depends on the context. Either way it is some form of a quotient set.
answered Feb 9 at 18:02
freakishfreakish
12.6k1630
edited Feb 9 at 18:10
answered Feb 9 at 18:02
freakishfreakish
12.6k1630
answered Feb 9 at 18:02
freakishfreakish
12.6k1630
answered Feb 9 at 18:02
freakishfreakish
12.6k1630
12.6k1630
$begingroup$
Also $mathbbR/mathbbQ$ can denote $mathbbR$ viewed as a field extension of $mathbbQ$.
$endgroup$
– AlephNull
Feb 9 at 22:46
add a comment |
$begingroup$
Also $mathbbR/mathbbQ$ can denote $mathbbR$ viewed as a field extension of $mathbbQ$.
$endgroup$
– AlephNull
Feb 9 at 22:46
$begingroup$
Also $mathbbR/mathbbQ$ can denote $mathbbR$ viewed as a field extension of $mathbbQ$.
$endgroup$
– AlephNull
Feb 9 at 22:46
$begingroup$
Also $mathbbR/mathbbQ$ can denote $mathbbR$ viewed as a field extension of $mathbbQ$.
$endgroup$
– AlephNull
Feb 9 at 22:46
add a comment |
$begingroup$
Depends on the context:
$mathbbR setminus mathbbQ$ is the set difference
between the reals and the rationals, so it equals the set of irrationals.
$mathbbR/mathbbQ$ can mean the quotient of the group of reals by its subgroup of the rationals, (which also gives a topological group) or it can denote a quotient space of the reals where we identify the subset of rationals to a single point.
answered Feb 9 at 18:02
Henno BrandsmaHenno Brandsma
111k348120
$endgroup$
add a comment |
$begingroup$
Depends on the context:
$mathbbR setminus mathbbQ$ is the set difference
between the reals and the rationals, so it equals the set of irrationals.
$mathbbR/mathbbQ$ can mean the quotient of the group of reals by its subgroup of the rationals, (which also gives a topological group) or it can denote a quotient space of the reals where we identify the subset of rationals to a single point.
answered Feb 9 at 18:02
Henno BrandsmaHenno Brandsma
111k348120
$endgroup$
add a comment |
$begingroup$
Depends on the context:
$mathbbR setminus mathbbQ$ is the set difference
between the reals and the rationals, so it equals the set of irrationals.
$mathbbR/mathbbQ$ can mean the quotient of the group of reals by its subgroup of the rationals, (which also gives a topological group) or it can denote a quotient space of the reals where we identify the subset of rationals to a single point.
answered Feb 9 at 18:02
Henno BrandsmaHenno Brandsma
111k348120
$endgroup$
Depends on the context:
$mathbbR setminus mathbbQ$ is the set difference
between the reals and the rationals, so it equals the set of irrationals.
$mathbbR/mathbbQ$ can mean the quotient of the group of reals by its subgroup of the rationals, (which also gives a topological group) or it can denote a quotient space of the reals where we identify the subset of rationals to a single point.
answered Feb 9 at 18:02
Henno BrandsmaHenno Brandsma
111k348120
answered Feb 9 at 18:02
Henno BrandsmaHenno Brandsma
111k348120
answered Feb 9 at 18:02
Henno BrandsmaHenno Brandsma
111k348120
answered Feb 9 at 18:02
Henno BrandsmaHenno Brandsma
111k348120
111k348120
add a comment |
add a comment |
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$begingroup$
Those are both versions of the "set difference", which is used probably determined by whichever notation is simpler to typeset. A/B= AB= the set of all elements of A that are NOT in B.
$endgroup$
– user247327
Feb 9 at 18:02
8
$begingroup$
@user247327 $A/B$ does not denote the set theoretic difference!
$endgroup$
– Alex Kruckman
Feb 9 at 18:20