Notation: subset of powerset containing sets of given cardinality
$begingroup$
We are given a set $S$. Is there a generally accepted symbol to denote the set of all subsets with cardinality $kappa$ of $S$? The notation that comes closest to what I want is the one I found on wikipedia:
https://en.wikipedia.org/wiki/Power_set#Subsets_of_limited_cardinality,
where they write:
``The set of subsets of $S$ of cardinality less than $kappa$ is denoted by $mathcal{P}_{kappa}(S)$ or $mathcal{P}_{<kappa}(S)$. Similarly, the set of non-empty subsets of S might be denoted by $mathcal{P}_{ge1}(S)$''
Is a notation like
$$mathcal{P}_{=kappa}(S)$$
generally accepted?
notation set-theory
edited Jan 8 at 14:26
bof
52.5k559121
asked May 10 '17 at 10:03
BJPrimBJPrim
526
$endgroup$
add a comment |
$begingroup$
We are given a set $S$. Is there a generally accepted symbol to denote the set of all subsets with cardinality $kappa$ of $S$? The notation that comes closest to what I want is the one I found on wikipedia:
https://en.wikipedia.org/wiki/Power_set#Subsets_of_limited_cardinality,
where they write:
``The set of subsets of $S$ of cardinality less than $kappa$ is denoted by $mathcal{P}_{kappa}(S)$ or $mathcal{P}_{<kappa}(S)$. Similarly, the set of non-empty subsets of S might be denoted by $mathcal{P}_{ge1}(S)$''
Is a notation like
$$mathcal{P}_{=kappa}(S)$$
generally accepted?
notation set-theory
edited Jan 8 at 14:26
bof
52.5k559121
asked May 10 '17 at 10:03
BJPrimBJPrim
526
$endgroup$
add a comment |
$begingroup$
We are given a set $S$. Is there a generally accepted symbol to denote the set of all subsets with cardinality $kappa$ of $S$? The notation that comes closest to what I want is the one I found on wikipedia:
https://en.wikipedia.org/wiki/Power_set#Subsets_of_limited_cardinality,
where they write:
``The set of subsets of $S$ of cardinality less than $kappa$ is denoted by $mathcal{P}_{kappa}(S)$ or $mathcal{P}_{<kappa}(S)$. Similarly, the set of non-empty subsets of S might be denoted by $mathcal{P}_{ge1}(S)$''
Is a notation like
$$mathcal{P}_{=kappa}(S)$$
generally accepted?
notation set-theory
edited Jan 8 at 14:26
bof
52.5k559121
asked May 10 '17 at 10:03
BJPrimBJPrim
526
$endgroup$
We are given a set $S$. Is there a generally accepted symbol to denote the set of all subsets with cardinality $kappa$ of $S$? The notation that comes closest to what I want is the one I found on wikipedia:
https://en.wikipedia.org/wiki/Power_set#Subsets_of_limited_cardinality,
where they write:
``The set of subsets of $S$ of cardinality less than $kappa$ is denoted by $mathcal{P}_{kappa}(S)$ or $mathcal{P}_{<kappa}(S)$. Similarly, the set of non-empty subsets of S might be denoted by $mathcal{P}_{ge1}(S)$''
Is a notation like
$$mathcal{P}_{=kappa}(S)$$
generally accepted?
notation set-theory
notation set-theory
edited Jan 8 at 14:26
bof
52.5k559121
asked May 10 '17 at 10:03
BJPrimBJPrim
526
edited Jan 8 at 14:26
bof
52.5k559121
asked May 10 '17 at 10:03
BJPrimBJPrim
526
edited Jan 8 at 14:26
bof
52.5k559121
edited Jan 8 at 14:26
bof
52.5k559121
edited Jan 8 at 14:26
bof
52.5k559121
52.5k559121
asked May 10 '17 at 10:03
BJPrimBJPrim
526
asked May 10 '17 at 10:03
BJPrimBJPrim
526
asked May 10 '17 at 10:03
BJPrimBJPrim
526
526
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I cannot say that I've seen that notation, but I am likely to understand it from context. A slightly more accepted notation is $[X]^kappa$.
But the usual advice in this situation is to explicitly define your notation if you feel it might be non-standard, and sometimes even if it is standard it is worth reminding the reader what exactly you mean.
answered May 10 '17 at 10:57
Asaf Karagila♦Asaf Karagila
307k33440773
$endgroup$
$begingroup$
OK thank you for the information. Now I am confident that explicitly defining my notation is the right thing to do here. Cheers!
$endgroup$
– BJPrim
May 11 '17 at 18:22
$begingroup$
@BJPrim Another notation iw $binom Skappa$ though come to think of it I've only seen that used for finite $kappa$, I'm not sure if it's in use for infinite $kappa$.
$endgroup$
– bof
Jan 8 at 14:29
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I cannot say that I've seen that notation, but I am likely to understand it from context. A slightly more accepted notation is $[X]^kappa$.
But the usual advice in this situation is to explicitly define your notation if you feel it might be non-standard, and sometimes even if it is standard it is worth reminding the reader what exactly you mean.
answered May 10 '17 at 10:57
Asaf Karagila♦Asaf Karagila
307k33440773
$endgroup$
$begingroup$
OK thank you for the information. Now I am confident that explicitly defining my notation is the right thing to do here. Cheers!
$endgroup$
– BJPrim
May 11 '17 at 18:22
$begingroup$
@BJPrim Another notation iw $binom Skappa$ though come to think of it I've only seen that used for finite $kappa$, I'm not sure if it's in use for infinite $kappa$.
$endgroup$
– bof
Jan 8 at 14:29
add a comment |
$begingroup$
I cannot say that I've seen that notation, but I am likely to understand it from context. A slightly more accepted notation is $[X]^kappa$.
But the usual advice in this situation is to explicitly define your notation if you feel it might be non-standard, and sometimes even if it is standard it is worth reminding the reader what exactly you mean.
answered May 10 '17 at 10:57
Asaf Karagila♦Asaf Karagila
307k33440773
$endgroup$
$begingroup$
OK thank you for the information. Now I am confident that explicitly defining my notation is the right thing to do here. Cheers!
$endgroup$
– BJPrim
May 11 '17 at 18:22
$begingroup$
@BJPrim Another notation iw $binom Skappa$ though come to think of it I've only seen that used for finite $kappa$, I'm not sure if it's in use for infinite $kappa$.
$endgroup$
– bof
Jan 8 at 14:29
add a comment |
$begingroup$
I cannot say that I've seen that notation, but I am likely to understand it from context. A slightly more accepted notation is $[X]^kappa$.
But the usual advice in this situation is to explicitly define your notation if you feel it might be non-standard, and sometimes even if it is standard it is worth reminding the reader what exactly you mean.
answered May 10 '17 at 10:57
Asaf Karagila♦Asaf Karagila
307k33440773
$endgroup$
I cannot say that I've seen that notation, but I am likely to understand it from context. A slightly more accepted notation is $[X]^kappa$.
But the usual advice in this situation is to explicitly define your notation if you feel it might be non-standard, and sometimes even if it is standard it is worth reminding the reader what exactly you mean.
answered May 10 '17 at 10:57
Asaf Karagila♦Asaf Karagila
307k33440773
answered May 10 '17 at 10:57
Asaf Karagila♦Asaf Karagila
307k33440773
answered May 10 '17 at 10:57
Asaf Karagila♦Asaf Karagila
307k33440773
answered May 10 '17 at 10:57
Asaf Karagila♦Asaf Karagila
307k33440773
307k33440773
$begingroup$
OK thank you for the information. Now I am confident that explicitly defining my notation is the right thing to do here. Cheers!
$endgroup$
– BJPrim
May 11 '17 at 18:22
$begingroup$
@BJPrim Another notation iw $binom Skappa$ though come to think of it I've only seen that used for finite $kappa$, I'm not sure if it's in use for infinite $kappa$.
$endgroup$
– bof
Jan 8 at 14:29
add a comment |
$begingroup$
OK thank you for the information. Now I am confident that explicitly defining my notation is the right thing to do here. Cheers!
$endgroup$
– BJPrim
May 11 '17 at 18:22
$begingroup$
@BJPrim Another notation iw $binom Skappa$ though come to think of it I've only seen that used for finite $kappa$, I'm not sure if it's in use for infinite $kappa$.
$endgroup$
– bof
Jan 8 at 14:29
$begingroup$
OK thank you for the information. Now I am confident that explicitly defining my notation is the right thing to do here. Cheers!
$endgroup$
– BJPrim
May 11 '17 at 18:22
$begingroup$
OK thank you for the information. Now I am confident that explicitly defining my notation is the right thing to do here. Cheers!
$endgroup$
– BJPrim
May 11 '17 at 18:22
$begingroup$
@BJPrim Another notation iw $binom Skappa$ though come to think of it I've only seen that used for finite $kappa$, I'm not sure if it's in use for infinite $kappa$.
$endgroup$
– bof
Jan 8 at 14:29
$begingroup$
@BJPrim Another notation iw $binom Skappa$ though come to think of it I've only seen that used for finite $kappa$, I'm not sure if it's in use for infinite $kappa$.
$endgroup$
– bof
Jan 8 at 14:29
add a comment |
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