Reference request: Set of n-Multisets of elements in $mathbbN$ is countable setWhy does mathematical convention deal so ineptly with multisets?Is $cap_n=1^infty left( mathbbR setminus A_n right) $ countable set?Prove that there exists a countable collection of rectangles in $mathbbR^n$Multisets and cardinalityAlgorithm for generating the intersection of two multisetsIs there a name for the infinite sequence of k-multisets with one element, two elements, etc.?Can I use inclusion symbol to address a multiset's elements?Arranging $mathbb N$ into a two-dimensional array to prove a countably infinite collection of countable sets is countable.Category of Multisets and SpansProof for bijection between the set of k-multisets & the set of k-subsets.
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Reference request: Set of n-Multisets of elements in $mathbbN$ is countable set
Why does mathematical convention deal so ineptly with multisets?Is $cap_n=1^infty left( mathbbR setminus A_n right) $ countable set?Prove that there exists a countable collection of rectangles in $mathbbR^n$Multisets and cardinalityAlgorithm for generating the intersection of two multisetsIs there a name for the infinite sequence of k-multisets with one element, two elements, etc.?Can I use inclusion symbol to address a multiset's elements?Arranging $mathbb N$ into a two-dimensional array to prove a countably infinite collection of countable sets is countable.Category of Multisets and SpansProof for bijection between the set of k-multisets & the set of k-subsets.
$begingroup$
Let $n in mathbbN$ be fixed. I need a reference for the statement, that the collection of multisets of length $n$ with elements in $mathbbN$
beginequation
M_mathbbN = a_i in mathbbN
endequation
is a set and is countable.
discrete-mathematics elementary-set-theory multisets
edited 2 days ago
Asaf Karagila♦
306k33438769
asked 2 days ago
warpfelwarpfel
1067
$endgroup$
add a comment |
$begingroup$
Let $n in mathbbN$ be fixed. I need a reference for the statement, that the collection of multisets of length $n$ with elements in $mathbbN$
beginequation
M_mathbbN = a_i in mathbbN
endequation
is a set and is countable.
discrete-mathematics elementary-set-theory multisets
edited 2 days ago
Asaf Karagila♦
306k33438769
asked 2 days ago
warpfelwarpfel
1067
$endgroup$
$begingroup$
There is a surjection from the finite sequences onto multisets.
$endgroup$
– Asaf Karagila♦
2 days ago
add a comment |
$begingroup$
Let $n in mathbbN$ be fixed. I need a reference for the statement, that the collection of multisets of length $n$ with elements in $mathbbN$
beginequation
M_mathbbN = a_i in mathbbN
endequation
is a set and is countable.
discrete-mathematics elementary-set-theory multisets
edited 2 days ago
Asaf Karagila♦
306k33438769
asked 2 days ago
warpfelwarpfel
1067
$endgroup$
Let $n in mathbbN$ be fixed. I need a reference for the statement, that the collection of multisets of length $n$ with elements in $mathbbN$
beginequation
M_mathbbN = a_i in mathbbN
endequation
is a set and is countable.
discrete-mathematics elementary-set-theory multisets
discrete-mathematics elementary-set-theory multisets
edited 2 days ago
Asaf Karagila♦
306k33438769
asked 2 days ago
warpfelwarpfel
1067
edited 2 days ago
Asaf Karagila♦
306k33438769
asked 2 days ago
warpfelwarpfel
1067
edited 2 days ago
Asaf Karagila♦
306k33438769
edited 2 days ago
Asaf Karagila♦
306k33438769
edited 2 days ago
Asaf Karagila♦
306k33438769
306k33438769
asked 2 days ago
warpfelwarpfel
1067
asked 2 days ago
warpfelwarpfel
1067
asked 2 days ago
warpfelwarpfel
1067
1067
$begingroup$
There is a surjection from the finite sequences onto multisets.
$endgroup$
– Asaf Karagila♦
2 days ago
add a comment |
$begingroup$
There is a surjection from the finite sequences onto multisets.
$endgroup$
– Asaf Karagila♦
2 days ago
$begingroup$
There is a surjection from the finite sequences onto multisets.
$endgroup$
– Asaf Karagila♦
2 days ago
$begingroup$
There is a surjection from the finite sequences onto multisets.
$endgroup$
– Asaf Karagila♦
2 days ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
There is a bijection $mathcalM_mathbbN rightarrow bigcup_k=0^inftymathbbN^k$. Now each $mathbbN^k$ is countable and countable unions of countable sets are again countable.
answered 2 days ago
An_876_JokeAn_876_Joke
1036
$endgroup$
add a comment |
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1 Answer
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oldest
votes
$begingroup$
There is a bijection $mathcalM_mathbbN rightarrow bigcup_k=0^inftymathbbN^k$. Now each $mathbbN^k$ is countable and countable unions of countable sets are again countable.
answered 2 days ago
An_876_JokeAn_876_Joke
1036
$endgroup$
add a comment |
$begingroup$
There is a bijection $mathcalM_mathbbN rightarrow bigcup_k=0^inftymathbbN^k$. Now each $mathbbN^k$ is countable and countable unions of countable sets are again countable.
answered 2 days ago
An_876_JokeAn_876_Joke
1036
$endgroup$
add a comment |
$begingroup$
There is a bijection $mathcalM_mathbbN rightarrow bigcup_k=0^inftymathbbN^k$. Now each $mathbbN^k$ is countable and countable unions of countable sets are again countable.
answered 2 days ago
An_876_JokeAn_876_Joke
1036
$endgroup$
There is a bijection $mathcalM_mathbbN rightarrow bigcup_k=0^inftymathbbN^k$. Now each $mathbbN^k$ is countable and countable unions of countable sets are again countable.
answered 2 days ago
An_876_JokeAn_876_Joke
1036
answered 2 days ago
An_876_JokeAn_876_Joke
1036
answered 2 days ago
An_876_JokeAn_876_Joke
1036
answered 2 days ago
An_876_JokeAn_876_Joke
1036
1036
add a comment |
add a comment |
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$begingroup$
There is a surjection from the finite sequences onto multisets.
$endgroup$
– Asaf Karagila♦
2 days ago