Notation for extracting value out of single element set
Clash Royale CLAN TAG#URR8PPP
$begingroup$
In some part of a document I am writing, I first define a set
$$
S : A to mathcal P(B) \
S(a) = textcomplicated expression here using $a$
$$
Later, I prove that $forall a,~exists x, ~S(a) = x $.
So, I want to now construct some notation for referring to the set with a single element $ x subset B$. Something like
$$unset(S(a))$$
where $unset$ is some valid definition / notation.
elementary-set-theory notation
asked Dec 29 '18 at 22:14
Siddharth BhatSiddharth Bhat
2,8581918
$endgroup$
add a comment |
$begingroup$
In some part of a document I am writing, I first define a set
$$
S : A to mathcal P(B) \
S(a) = textcomplicated expression here using $a$
$$
Later, I prove that $forall a,~exists x, ~S(a) = x $.
So, I want to now construct some notation for referring to the set with a single element $ x subset B$. Something like
$$unset(S(a))$$
where $unset$ is some valid definition / notation.
elementary-set-theory notation
asked Dec 29 '18 at 22:14
Siddharth BhatSiddharth Bhat
2,8581918
$endgroup$
1
$begingroup$
If $S(a) =x$ is guaranteed to be a singleton, then people will often abuse notation a bit by pretending that $S(a) = x$. In other words, both $x$ and $x$ are denoted as $S(a)$ (and hopefully the meaning is clear from context).
$endgroup$
– littleO
Dec 29 '18 at 23:58
add a comment |
$begingroup$
In some part of a document I am writing, I first define a set
$$
S : A to mathcal P(B) \
S(a) = textcomplicated expression here using $a$
$$
Later, I prove that $forall a,~exists x, ~S(a) = x $.
So, I want to now construct some notation for referring to the set with a single element $ x subset B$. Something like
$$unset(S(a))$$
where $unset$ is some valid definition / notation.
elementary-set-theory notation
asked Dec 29 '18 at 22:14
Siddharth BhatSiddharth Bhat
2,8581918
$endgroup$
In some part of a document I am writing, I first define a set
$$
S : A to mathcal P(B) \
S(a) = textcomplicated expression here using $a$
$$
Later, I prove that $forall a,~exists x, ~S(a) = x $.
So, I want to now construct some notation for referring to the set with a single element $ x subset B$. Something like
$$unset(S(a))$$
where $unset$ is some valid definition / notation.
elementary-set-theory notation
elementary-set-theory notation
asked Dec 29 '18 at 22:14
Siddharth BhatSiddharth Bhat
2,8581918
asked Dec 29 '18 at 22:14
Siddharth BhatSiddharth Bhat
2,8581918
asked Dec 29 '18 at 22:14
Siddharth BhatSiddharth Bhat
2,8581918
asked Dec 29 '18 at 22:14
Siddharth BhatSiddharth Bhat
2,8581918
asked Dec 29 '18 at 22:14
Siddharth BhatSiddharth Bhat
2,8581918
2,8581918
1
$begingroup$
If $S(a) =x$ is guaranteed to be a singleton, then people will often abuse notation a bit by pretending that $S(a) = x$. In other words, both $x$ and $x$ are denoted as $S(a)$ (and hopefully the meaning is clear from context).
$endgroup$
– littleO
Dec 29 '18 at 23:58
add a comment |
1
$begingroup$
If $S(a) =x$ is guaranteed to be a singleton, then people will often abuse notation a bit by pretending that $S(a) = x$. In other words, both $x$ and $x$ are denoted as $S(a)$ (and hopefully the meaning is clear from context).
$endgroup$
– littleO
Dec 29 '18 at 23:58
1
1
$begingroup$
If $S(a) =x$ is guaranteed to be a singleton, then people will often abuse notation a bit by pretending that $S(a) = x$. In other words, both $x$ and $x$ are denoted as $S(a)$ (and hopefully the meaning is clear from context).
$endgroup$
– littleO
Dec 29 '18 at 23:58
$begingroup$
If $S(a) =x$ is guaranteed to be a singleton, then people will often abuse notation a bit by pretending that $S(a) = x$. In other words, both $x$ and $x$ are denoted as $S(a)$ (and hopefully the meaning is clear from context).
$endgroup$
– littleO
Dec 29 '18 at 23:58
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
There is no commonly used notation specifically for this, so you shouldn't hesitate to just make up your own. One way you can express it with standard notation is with the symbol $bigcup$: if $S$ is a set, then $bigcup S$ denotes the union of all the elements of $S$, so $bigcup x=x$. This is kind of a "hack" though and is not something you can expect your readers to effortlessly understand. (Mathematically literate readers will figure it out, but it may take them a little work.)
Ultimately, the purpose of notation is to communicate, so you should pick your notation to communicate clearly and not be afraid to use words instead of notation if that would be clearer. I would probably recommend instead just writing something like:
We write $s(a)$ for the unique element of the set $S(a)$.
There's nothing special about the choice of $s$ as the function name for this; it's a reasonable choice to use to remind the reader that it is related to $S$ but there's nothing wrong with using a different name if you have a better reason.
answered Dec 29 '18 at 22:32
Eric WofseyEric Wofsey
181k12208336
$endgroup$
$begingroup$
Thank you, I suppose I'll just do that then :) I was hoping for some existing notation, but oh well.
$endgroup$
– Siddharth Bhat
Dec 29 '18 at 22:34
$begingroup$
I have doubts regarding the validity of blindly using this notation. I think that implicitly the union must be over a collection of sets. If not then what the heck would $2cup 3$ possibly mean?
$endgroup$
– MPW
Dec 29 '18 at 23:11
$begingroup$
@MPW Remember that $2=,$, so it's perfectly meaningful. :P (At least, if we're working in set theory.) More to the point, as long as the OP doesn't write "$bigcup x$" when $x$ isn't a set, they'll be fine. And actually, even outside of ZFC you can arguably make sense of all such expressions: e.g. "$2cup3$" is by definition $x: xin 2$ or $xin3$, and if $2$ has no elements this is just $3$. :P
$endgroup$
– Noah Schweber
Dec 29 '18 at 23:26
$begingroup$
@NoahSchweber : I can’t accept that. Here I refer to the union of a point (i.e. a non-set) with a set. That’s meaningless. I also do not accept the notion that $xmid xin y$ is meaningful if $y$ is not a set, so it certainly isn’t just $varnothing$ because you can’t find any elements in $y$. The very notation is meaningless, just like writing “5 + banana” where “banana” really is a banana.
$endgroup$
– MPW
Dec 29 '18 at 23:40
$begingroup$
@MPW "Here I refer to the union of a point (i.e. a non-set) with a set." I know - I'm saying that "$xin y$" can be viewed as making perfect sense even if $y$ isn't a set: if $y$ isn't a set, then no matter what $x$ is the statement "$xin y$" is false. This is a perfectly coherent, if silly, way to approach things. And the ZFC approach moots the entire issue by making everything a set. But all this is beside the point, which is that this notation poses no danger to the OP: they're only writing "$bigcup x$" in case $x$ is a set (namely, one of the $S(a)$s) so the issue won't even come up.
$endgroup$
– Noah Schweber
Dec 29 '18 at 23:49
|
show 1 more comment
$begingroup$
It is just the union:
$$bigcup S(a) = bigcupx = x$$
Indeed, the union of a set $A$ is defined with $$c in bigcup A iff exists D in A text such that c in D$$
For two sets we have the more familiar notation $A cup B = bigcup A,B$.
answered Dec 29 '18 at 22:22
mechanodroidmechanodroid
27.1k62446
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1
$begingroup$
This is true but I wouldn't necessarily recommend actually using this notation--it is not particularly evocative of the desired meaning here and may confuse some readers.
$endgroup$
– Eric Wofsey
Dec 29 '18 at 22:23
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@EricWofsey Agreed, I wouldn't use any kind of "$textunset$" function. It would be best to state that $S(a) = x$ and then just use $x$.
$endgroup$
– mechanodroid
Dec 29 '18 at 22:27
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This is neat, I would not have thought of that! However, I'm accepting Eric's answer, since I believe it answers the question's spirit better, by suggesting some kind of wording.
$endgroup$
– Siddharth Bhat
Dec 29 '18 at 22:34
add a comment |
$begingroup$
Since it looks like you’re going to have to invent your own notation, why not just simply $hata$ ? Why bring $S$ into the notation at all?
answered Dec 29 '18 at 23:03
MPWMPW
29.9k12056
$endgroup$
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
There is no commonly used notation specifically for this, so you shouldn't hesitate to just make up your own. One way you can express it with standard notation is with the symbol $bigcup$: if $S$ is a set, then $bigcup S$ denotes the union of all the elements of $S$, so $bigcup x=x$. This is kind of a "hack" though and is not something you can expect your readers to effortlessly understand. (Mathematically literate readers will figure it out, but it may take them a little work.)
Ultimately, the purpose of notation is to communicate, so you should pick your notation to communicate clearly and not be afraid to use words instead of notation if that would be clearer. I would probably recommend instead just writing something like:
We write $s(a)$ for the unique element of the set $S(a)$.
There's nothing special about the choice of $s$ as the function name for this; it's a reasonable choice to use to remind the reader that it is related to $S$ but there's nothing wrong with using a different name if you have a better reason.
answered Dec 29 '18 at 22:32
Eric WofseyEric Wofsey
181k12208336
$endgroup$
$begingroup$
Thank you, I suppose I'll just do that then :) I was hoping for some existing notation, but oh well.
$endgroup$
– Siddharth Bhat
Dec 29 '18 at 22:34
$begingroup$
I have doubts regarding the validity of blindly using this notation. I think that implicitly the union must be over a collection of sets. If not then what the heck would $2cup 3$ possibly mean?
$endgroup$
– MPW
Dec 29 '18 at 23:11
$begingroup$
@MPW Remember that $2=,$, so it's perfectly meaningful. :P (At least, if we're working in set theory.) More to the point, as long as the OP doesn't write "$bigcup x$" when $x$ isn't a set, they'll be fine. And actually, even outside of ZFC you can arguably make sense of all such expressions: e.g. "$2cup3$" is by definition $x: xin 2$ or $xin3$, and if $2$ has no elements this is just $3$. :P
$endgroup$
– Noah Schweber
Dec 29 '18 at 23:26
$begingroup$
@NoahSchweber : I can’t accept that. Here I refer to the union of a point (i.e. a non-set) with a set. That’s meaningless. I also do not accept the notion that $xmid xin y$ is meaningful if $y$ is not a set, so it certainly isn’t just $varnothing$ because you can’t find any elements in $y$. The very notation is meaningless, just like writing “5 + banana” where “banana” really is a banana.
$endgroup$
– MPW
Dec 29 '18 at 23:40
$begingroup$
@MPW "Here I refer to the union of a point (i.e. a non-set) with a set." I know - I'm saying that "$xin y$" can be viewed as making perfect sense even if $y$ isn't a set: if $y$ isn't a set, then no matter what $x$ is the statement "$xin y$" is false. This is a perfectly coherent, if silly, way to approach things. And the ZFC approach moots the entire issue by making everything a set. But all this is beside the point, which is that this notation poses no danger to the OP: they're only writing "$bigcup x$" in case $x$ is a set (namely, one of the $S(a)$s) so the issue won't even come up.
$endgroup$
– Noah Schweber
Dec 29 '18 at 23:49
|
show 1 more comment
$begingroup$
There is no commonly used notation specifically for this, so you shouldn't hesitate to just make up your own. One way you can express it with standard notation is with the symbol $bigcup$: if $S$ is a set, then $bigcup S$ denotes the union of all the elements of $S$, so $bigcup x=x$. This is kind of a "hack" though and is not something you can expect your readers to effortlessly understand. (Mathematically literate readers will figure it out, but it may take them a little work.)
Ultimately, the purpose of notation is to communicate, so you should pick your notation to communicate clearly and not be afraid to use words instead of notation if that would be clearer. I would probably recommend instead just writing something like:
We write $s(a)$ for the unique element of the set $S(a)$.
There's nothing special about the choice of $s$ as the function name for this; it's a reasonable choice to use to remind the reader that it is related to $S$ but there's nothing wrong with using a different name if you have a better reason.
answered Dec 29 '18 at 22:32
Eric WofseyEric Wofsey
181k12208336
$endgroup$
$begingroup$
Thank you, I suppose I'll just do that then :) I was hoping for some existing notation, but oh well.
$endgroup$
– Siddharth Bhat
Dec 29 '18 at 22:34
$begingroup$
I have doubts regarding the validity of blindly using this notation. I think that implicitly the union must be over a collection of sets. If not then what the heck would $2cup 3$ possibly mean?
$endgroup$
– MPW
Dec 29 '18 at 23:11
$begingroup$
@MPW Remember that $2=,$, so it's perfectly meaningful. :P (At least, if we're working in set theory.) More to the point, as long as the OP doesn't write "$bigcup x$" when $x$ isn't a set, they'll be fine. And actually, even outside of ZFC you can arguably make sense of all such expressions: e.g. "$2cup3$" is by definition $x: xin 2$ or $xin3$, and if $2$ has no elements this is just $3$. :P
$endgroup$
– Noah Schweber
Dec 29 '18 at 23:26
$begingroup$
@NoahSchweber : I can’t accept that. Here I refer to the union of a point (i.e. a non-set) with a set. That’s meaningless. I also do not accept the notion that $xmid xin y$ is meaningful if $y$ is not a set, so it certainly isn’t just $varnothing$ because you can’t find any elements in $y$. The very notation is meaningless, just like writing “5 + banana” where “banana” really is a banana.
$endgroup$
– MPW
Dec 29 '18 at 23:40
$begingroup$
@MPW "Here I refer to the union of a point (i.e. a non-set) with a set." I know - I'm saying that "$xin y$" can be viewed as making perfect sense even if $y$ isn't a set: if $y$ isn't a set, then no matter what $x$ is the statement "$xin y$" is false. This is a perfectly coherent, if silly, way to approach things. And the ZFC approach moots the entire issue by making everything a set. But all this is beside the point, which is that this notation poses no danger to the OP: they're only writing "$bigcup x$" in case $x$ is a set (namely, one of the $S(a)$s) so the issue won't even come up.
$endgroup$
– Noah Schweber
Dec 29 '18 at 23:49
|
show 1 more comment
$begingroup$
There is no commonly used notation specifically for this, so you shouldn't hesitate to just make up your own. One way you can express it with standard notation is with the symbol $bigcup$: if $S$ is a set, then $bigcup S$ denotes the union of all the elements of $S$, so $bigcup x=x$. This is kind of a "hack" though and is not something you can expect your readers to effortlessly understand. (Mathematically literate readers will figure it out, but it may take them a little work.)
Ultimately, the purpose of notation is to communicate, so you should pick your notation to communicate clearly and not be afraid to use words instead of notation if that would be clearer. I would probably recommend instead just writing something like:
We write $s(a)$ for the unique element of the set $S(a)$.
There's nothing special about the choice of $s$ as the function name for this; it's a reasonable choice to use to remind the reader that it is related to $S$ but there's nothing wrong with using a different name if you have a better reason.
answered Dec 29 '18 at 22:32
Eric WofseyEric Wofsey
181k12208336
$endgroup$
There is no commonly used notation specifically for this, so you shouldn't hesitate to just make up your own. One way you can express it with standard notation is with the symbol $bigcup$: if $S$ is a set, then $bigcup S$ denotes the union of all the elements of $S$, so $bigcup x=x$. This is kind of a "hack" though and is not something you can expect your readers to effortlessly understand. (Mathematically literate readers will figure it out, but it may take them a little work.)
Ultimately, the purpose of notation is to communicate, so you should pick your notation to communicate clearly and not be afraid to use words instead of notation if that would be clearer. I would probably recommend instead just writing something like:
We write $s(a)$ for the unique element of the set $S(a)$.
There's nothing special about the choice of $s$ as the function name for this; it's a reasonable choice to use to remind the reader that it is related to $S$ but there's nothing wrong with using a different name if you have a better reason.
answered Dec 29 '18 at 22:32
Eric WofseyEric Wofsey
181k12208336
edited Dec 29 '18 at 22:35
answered Dec 29 '18 at 22:32
Eric WofseyEric Wofsey
181k12208336
answered Dec 29 '18 at 22:32
Eric WofseyEric Wofsey
181k12208336
answered Dec 29 '18 at 22:32
Eric WofseyEric Wofsey
181k12208336
181k12208336
$begingroup$
Thank you, I suppose I'll just do that then :) I was hoping for some existing notation, but oh well.
$endgroup$
– Siddharth Bhat
Dec 29 '18 at 22:34
$begingroup$
I have doubts regarding the validity of blindly using this notation. I think that implicitly the union must be over a collection of sets. If not then what the heck would $2cup 3$ possibly mean?
$endgroup$
– MPW
Dec 29 '18 at 23:11
$begingroup$
@MPW Remember that $2=,$, so it's perfectly meaningful. :P (At least, if we're working in set theory.) More to the point, as long as the OP doesn't write "$bigcup x$" when $x$ isn't a set, they'll be fine. And actually, even outside of ZFC you can arguably make sense of all such expressions: e.g. "$2cup3$" is by definition $x: xin 2$ or $xin3$, and if $2$ has no elements this is just $3$. :P
$endgroup$
– Noah Schweber
Dec 29 '18 at 23:26
$begingroup$
@NoahSchweber : I can’t accept that. Here I refer to the union of a point (i.e. a non-set) with a set. That’s meaningless. I also do not accept the notion that $xmid xin y$ is meaningful if $y$ is not a set, so it certainly isn’t just $varnothing$ because you can’t find any elements in $y$. The very notation is meaningless, just like writing “5 + banana” where “banana” really is a banana.
$endgroup$
– MPW
Dec 29 '18 at 23:40
$begingroup$
@MPW "Here I refer to the union of a point (i.e. a non-set) with a set." I know - I'm saying that "$xin y$" can be viewed as making perfect sense even if $y$ isn't a set: if $y$ isn't a set, then no matter what $x$ is the statement "$xin y$" is false. This is a perfectly coherent, if silly, way to approach things. And the ZFC approach moots the entire issue by making everything a set. But all this is beside the point, which is that this notation poses no danger to the OP: they're only writing "$bigcup x$" in case $x$ is a set (namely, one of the $S(a)$s) so the issue won't even come up.
$endgroup$
– Noah Schweber
Dec 29 '18 at 23:49
|
show 1 more comment
$begingroup$
Thank you, I suppose I'll just do that then :) I was hoping for some existing notation, but oh well.
$endgroup$
– Siddharth Bhat
Dec 29 '18 at 22:34
$begingroup$
I have doubts regarding the validity of blindly using this notation. I think that implicitly the union must be over a collection of sets. If not then what the heck would $2cup 3$ possibly mean?
$endgroup$
– MPW
Dec 29 '18 at 23:11
$begingroup$
@MPW Remember that $2=,$, so it's perfectly meaningful. :P (At least, if we're working in set theory.) More to the point, as long as the OP doesn't write "$bigcup x$" when $x$ isn't a set, they'll be fine. And actually, even outside of ZFC you can arguably make sense of all such expressions: e.g. "$2cup3$" is by definition $x: xin 2$ or $xin3$, and if $2$ has no elements this is just $3$. :P
$endgroup$
– Noah Schweber
Dec 29 '18 at 23:26
$begingroup$
@NoahSchweber : I can’t accept that. Here I refer to the union of a point (i.e. a non-set) with a set. That’s meaningless. I also do not accept the notion that $xmid xin y$ is meaningful if $y$ is not a set, so it certainly isn’t just $varnothing$ because you can’t find any elements in $y$. The very notation is meaningless, just like writing “5 + banana” where “banana” really is a banana.
$endgroup$
– MPW
Dec 29 '18 at 23:40
$begingroup$
@MPW "Here I refer to the union of a point (i.e. a non-set) with a set." I know - I'm saying that "$xin y$" can be viewed as making perfect sense even if $y$ isn't a set: if $y$ isn't a set, then no matter what $x$ is the statement "$xin y$" is false. This is a perfectly coherent, if silly, way to approach things. And the ZFC approach moots the entire issue by making everything a set. But all this is beside the point, which is that this notation poses no danger to the OP: they're only writing "$bigcup x$" in case $x$ is a set (namely, one of the $S(a)$s) so the issue won't even come up.
$endgroup$
– Noah Schweber
Dec 29 '18 at 23:49
$begingroup$
Thank you, I suppose I'll just do that then :) I was hoping for some existing notation, but oh well.
$endgroup$
– Siddharth Bhat
Dec 29 '18 at 22:34
$begingroup$
Thank you, I suppose I'll just do that then :) I was hoping for some existing notation, but oh well.
$endgroup$
– Siddharth Bhat
Dec 29 '18 at 22:34
$begingroup$
I have doubts regarding the validity of blindly using this notation. I think that implicitly the union must be over a collection of sets. If not then what the heck would $2cup 3$ possibly mean?
$endgroup$
– MPW
Dec 29 '18 at 23:11
$begingroup$
I have doubts regarding the validity of blindly using this notation. I think that implicitly the union must be over a collection of sets. If not then what the heck would $2cup 3$ possibly mean?
$endgroup$
– MPW
Dec 29 '18 at 23:11
$begingroup$
@MPW Remember that $2=,$, so it's perfectly meaningful. :P (At least, if we're working in set theory.) More to the point, as long as the OP doesn't write "$bigcup x$" when $x$ isn't a set, they'll be fine. And actually, even outside of ZFC you can arguably make sense of all such expressions: e.g. "$2cup3$" is by definition $x: xin 2$ or $xin3$, and if $2$ has no elements this is just $3$. :P
$endgroup$
– Noah Schweber
Dec 29 '18 at 23:26
$begingroup$
@MPW Remember that $2=,$, so it's perfectly meaningful. :P (At least, if we're working in set theory.) More to the point, as long as the OP doesn't write "$bigcup x$" when $x$ isn't a set, they'll be fine. And actually, even outside of ZFC you can arguably make sense of all such expressions: e.g. "$2cup3$" is by definition $x: xin 2$ or $xin3$, and if $2$ has no elements this is just $3$. :P
$endgroup$
– Noah Schweber
Dec 29 '18 at 23:26
$begingroup$
@NoahSchweber : I can’t accept that. Here I refer to the union of a point (i.e. a non-set) with a set. That’s meaningless. I also do not accept the notion that $xmid xin y$ is meaningful if $y$ is not a set, so it certainly isn’t just $varnothing$ because you can’t find any elements in $y$. The very notation is meaningless, just like writing “5 + banana” where “banana” really is a banana.
$endgroup$
– MPW
Dec 29 '18 at 23:40
$begingroup$
@NoahSchweber : I can’t accept that. Here I refer to the union of a point (i.e. a non-set) with a set. That’s meaningless. I also do not accept the notion that $xmid xin y$ is meaningful if $y$ is not a set, so it certainly isn’t just $varnothing$ because you can’t find any elements in $y$. The very notation is meaningless, just like writing “5 + banana” where “banana” really is a banana.
$endgroup$
– MPW
Dec 29 '18 at 23:40
$begingroup$
@MPW "Here I refer to the union of a point (i.e. a non-set) with a set." I know - I'm saying that "$xin y$" can be viewed as making perfect sense even if $y$ isn't a set: if $y$ isn't a set, then no matter what $x$ is the statement "$xin y$" is false. This is a perfectly coherent, if silly, way to approach things. And the ZFC approach moots the entire issue by making everything a set. But all this is beside the point, which is that this notation poses no danger to the OP: they're only writing "$bigcup x$" in case $x$ is a set (namely, one of the $S(a)$s) so the issue won't even come up.
$endgroup$
– Noah Schweber
Dec 29 '18 at 23:49
$begingroup$
@MPW "Here I refer to the union of a point (i.e. a non-set) with a set." I know - I'm saying that "$xin y$" can be viewed as making perfect sense even if $y$ isn't a set: if $y$ isn't a set, then no matter what $x$ is the statement "$xin y$" is false. This is a perfectly coherent, if silly, way to approach things. And the ZFC approach moots the entire issue by making everything a set. But all this is beside the point, which is that this notation poses no danger to the OP: they're only writing "$bigcup x$" in case $x$ is a set (namely, one of the $S(a)$s) so the issue won't even come up.
$endgroup$
– Noah Schweber
Dec 29 '18 at 23:49
|
show 1 more comment
$begingroup$
It is just the union:
$$bigcup S(a) = bigcupx = x$$
Indeed, the union of a set $A$ is defined with $$c in bigcup A iff exists D in A text such that c in D$$
For two sets we have the more familiar notation $A cup B = bigcup A,B$.
answered Dec 29 '18 at 22:22
mechanodroidmechanodroid
27.1k62446
$endgroup$
1
$begingroup$
This is true but I wouldn't necessarily recommend actually using this notation--it is not particularly evocative of the desired meaning here and may confuse some readers.
$endgroup$
– Eric Wofsey
Dec 29 '18 at 22:23
$begingroup$
@EricWofsey Agreed, I wouldn't use any kind of "$textunset$" function. It would be best to state that $S(a) = x$ and then just use $x$.
$endgroup$
– mechanodroid
Dec 29 '18 at 22:27
$begingroup$
This is neat, I would not have thought of that! However, I'm accepting Eric's answer, since I believe it answers the question's spirit better, by suggesting some kind of wording.
$endgroup$
– Siddharth Bhat
Dec 29 '18 at 22:34
add a comment |
$begingroup$
It is just the union:
$$bigcup S(a) = bigcupx = x$$
Indeed, the union of a set $A$ is defined with $$c in bigcup A iff exists D in A text such that c in D$$
For two sets we have the more familiar notation $A cup B = bigcup A,B$.
answered Dec 29 '18 at 22:22
mechanodroidmechanodroid
27.1k62446
$endgroup$
1
$begingroup$
This is true but I wouldn't necessarily recommend actually using this notation--it is not particularly evocative of the desired meaning here and may confuse some readers.
$endgroup$
– Eric Wofsey
Dec 29 '18 at 22:23
$begingroup$
@EricWofsey Agreed, I wouldn't use any kind of "$textunset$" function. It would be best to state that $S(a) = x$ and then just use $x$.
$endgroup$
– mechanodroid
Dec 29 '18 at 22:27
$begingroup$
This is neat, I would not have thought of that! However, I'm accepting Eric's answer, since I believe it answers the question's spirit better, by suggesting some kind of wording.
$endgroup$
– Siddharth Bhat
Dec 29 '18 at 22:34
add a comment |
$begingroup$
It is just the union:
$$bigcup S(a) = bigcupx = x$$
Indeed, the union of a set $A$ is defined with $$c in bigcup A iff exists D in A text such that c in D$$
For two sets we have the more familiar notation $A cup B = bigcup A,B$.
answered Dec 29 '18 at 22:22
mechanodroidmechanodroid
27.1k62446
$endgroup$
It is just the union:
$$bigcup S(a) = bigcupx = x$$
Indeed, the union of a set $A$ is defined with $$c in bigcup A iff exists D in A text such that c in D$$
For two sets we have the more familiar notation $A cup B = bigcup A,B$.
answered Dec 29 '18 at 22:22
mechanodroidmechanodroid
27.1k62446
answered Dec 29 '18 at 22:22
mechanodroidmechanodroid
27.1k62446
answered Dec 29 '18 at 22:22
mechanodroidmechanodroid
27.1k62446
answered Dec 29 '18 at 22:22
mechanodroidmechanodroid
27.1k62446
27.1k62446
1
$begingroup$
This is true but I wouldn't necessarily recommend actually using this notation--it is not particularly evocative of the desired meaning here and may confuse some readers.
$endgroup$
– Eric Wofsey
Dec 29 '18 at 22:23
$begingroup$
@EricWofsey Agreed, I wouldn't use any kind of "$textunset$" function. It would be best to state that $S(a) = x$ and then just use $x$.
$endgroup$
– mechanodroid
Dec 29 '18 at 22:27
$begingroup$
This is neat, I would not have thought of that! However, I'm accepting Eric's answer, since I believe it answers the question's spirit better, by suggesting some kind of wording.
$endgroup$
– Siddharth Bhat
Dec 29 '18 at 22:34
add a comment |
1
$begingroup$
This is true but I wouldn't necessarily recommend actually using this notation--it is not particularly evocative of the desired meaning here and may confuse some readers.
$endgroup$
– Eric Wofsey
Dec 29 '18 at 22:23
$begingroup$
@EricWofsey Agreed, I wouldn't use any kind of "$textunset$" function. It would be best to state that $S(a) = x$ and then just use $x$.
$endgroup$
– mechanodroid
Dec 29 '18 at 22:27
$begingroup$
This is neat, I would not have thought of that! However, I'm accepting Eric's answer, since I believe it answers the question's spirit better, by suggesting some kind of wording.
$endgroup$
– Siddharth Bhat
Dec 29 '18 at 22:34
1
1
$begingroup$
This is true but I wouldn't necessarily recommend actually using this notation--it is not particularly evocative of the desired meaning here and may confuse some readers.
$endgroup$
– Eric Wofsey
Dec 29 '18 at 22:23
$begingroup$
This is true but I wouldn't necessarily recommend actually using this notation--it is not particularly evocative of the desired meaning here and may confuse some readers.
$endgroup$
– Eric Wofsey
Dec 29 '18 at 22:23
$begingroup$
@EricWofsey Agreed, I wouldn't use any kind of "$textunset$" function. It would be best to state that $S(a) = x$ and then just use $x$.
$endgroup$
– mechanodroid
Dec 29 '18 at 22:27
$begingroup$
@EricWofsey Agreed, I wouldn't use any kind of "$textunset$" function. It would be best to state that $S(a) = x$ and then just use $x$.
$endgroup$
– mechanodroid
Dec 29 '18 at 22:27
$begingroup$
This is neat, I would not have thought of that! However, I'm accepting Eric's answer, since I believe it answers the question's spirit better, by suggesting some kind of wording.
$endgroup$
– Siddharth Bhat
Dec 29 '18 at 22:34
$begingroup$
This is neat, I would not have thought of that! However, I'm accepting Eric's answer, since I believe it answers the question's spirit better, by suggesting some kind of wording.
$endgroup$
– Siddharth Bhat
Dec 29 '18 at 22:34
add a comment |
$begingroup$
Since it looks like you’re going to have to invent your own notation, why not just simply $hata$ ? Why bring $S$ into the notation at all?
answered Dec 29 '18 at 23:03
MPWMPW
29.9k12056
$endgroup$
add a comment |
$begingroup$
Since it looks like you’re going to have to invent your own notation, why not just simply $hata$ ? Why bring $S$ into the notation at all?
answered Dec 29 '18 at 23:03
MPWMPW
29.9k12056
$endgroup$
add a comment |
$begingroup$
Since it looks like you’re going to have to invent your own notation, why not just simply $hata$ ? Why bring $S$ into the notation at all?
answered Dec 29 '18 at 23:03
MPWMPW
29.9k12056
$endgroup$
Since it looks like you’re going to have to invent your own notation, why not just simply $hata$ ? Why bring $S$ into the notation at all?
answered Dec 29 '18 at 23:03
MPWMPW
29.9k12056
answered Dec 29 '18 at 23:03
MPWMPW
29.9k12056
answered Dec 29 '18 at 23:03
MPWMPW
29.9k12056
answered Dec 29 '18 at 23:03
MPWMPW
29.9k12056
29.9k12056
add a comment |
add a comment |
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If $S(a) =x$ is guaranteed to be a singleton, then people will often abuse notation a bit by pretending that $S(a) = x$. In other words, both $x$ and $x$ are denoted as $S(a)$ (and hopefully the meaning is clear from context).
$endgroup$
– littleO
Dec 29 '18 at 23:58