Uncountable sets unrelated to real numbers
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The question may be a little general, but are there any other examples of uncountable sets except those related to real numbers?
elementary-set-theory
asked Jan 14 at 12:44
Cebiş MellimCebiş Mellim
18612
$endgroup$
add a comment |
$begingroup$
The question may be a little general, but are there any other examples of uncountable sets except those related to real numbers?
elementary-set-theory
asked Jan 14 at 12:44
Cebiş MellimCebiş Mellim
18612
$endgroup$
1
$begingroup$
The set of subsets (i.e. power-set) of every countable infinite set.
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– Mauro ALLEGRANZA
Jan 14 at 12:47
1
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The set of all functions from $mathbb{N}tomathbb{N}$ is always an interesting example.
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– user3482749
Jan 14 at 12:48
1
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I like the first uncountable ordinal
$endgroup$
– Questioner
Jan 14 at 13:52
add a comment |
$begingroup$
The question may be a little general, but are there any other examples of uncountable sets except those related to real numbers?
elementary-set-theory
asked Jan 14 at 12:44
Cebiş MellimCebiş Mellim
18612
$endgroup$
The question may be a little general, but are there any other examples of uncountable sets except those related to real numbers?
elementary-set-theory
elementary-set-theory
asked Jan 14 at 12:44
Cebiş MellimCebiş Mellim
18612
asked Jan 14 at 12:44
Cebiş MellimCebiş Mellim
18612
asked Jan 14 at 12:44
Cebiş MellimCebiş Mellim
18612
asked Jan 14 at 12:44
Cebiş MellimCebiş Mellim
18612
asked Jan 14 at 12:44
Cebiş MellimCebiş Mellim
18612
18612
1
$begingroup$
The set of subsets (i.e. power-set) of every countable infinite set.
$endgroup$
– Mauro ALLEGRANZA
Jan 14 at 12:47
1
$begingroup$
The set of all functions from $mathbb{N}tomathbb{N}$ is always an interesting example.
$endgroup$
– user3482749
Jan 14 at 12:48
1
$begingroup$
I like the first uncountable ordinal
$endgroup$
– Questioner
Jan 14 at 13:52
add a comment |
1
$begingroup$
The set of subsets (i.e. power-set) of every countable infinite set.
$endgroup$
– Mauro ALLEGRANZA
Jan 14 at 12:47
1
$begingroup$
The set of all functions from $mathbb{N}tomathbb{N}$ is always an interesting example.
$endgroup$
– user3482749
Jan 14 at 12:48
1
$begingroup$
I like the first uncountable ordinal
$endgroup$
– Questioner
Jan 14 at 13:52
1
1
$begingroup$
The set of subsets (i.e. power-set) of every countable infinite set.
$endgroup$
– Mauro ALLEGRANZA
Jan 14 at 12:47
$begingroup$
The set of subsets (i.e. power-set) of every countable infinite set.
$endgroup$
– Mauro ALLEGRANZA
Jan 14 at 12:47
1
1
$begingroup$
The set of all functions from $mathbb{N}tomathbb{N}$ is always an interesting example.
$endgroup$
– user3482749
Jan 14 at 12:48
$begingroup$
The set of all functions from $mathbb{N}tomathbb{N}$ is always an interesting example.
$endgroup$
– user3482749
Jan 14 at 12:48
1
1
$begingroup$
I like the first uncountable ordinal
$endgroup$
– Questioner
Jan 14 at 13:52
$begingroup$
I like the first uncountable ordinal
$endgroup$
– Questioner
Jan 14 at 13:52
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The set
$$ {(x_n): x_n in {0,1} quad forall n in mathbb N}$$
is uncountable.
answered Jan 14 at 12:55
FredFred
48.7k11849
$endgroup$
add a comment |
$begingroup$
There are many.
The fist one to come to mind is the first uncountable ordinal. It is so unrelated to the real numbers that trying to come up with a useful relationship at all between the two was allegedly what drove Georg Cantor mad. There are, of course, any ordinal above that one as well.
As mentioned in the comments, the power-set of any infinite set is uncountably infinite.
answered Jan 14 at 12:50
ArthurArthur
119k7119202
$endgroup$
add a comment |
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$begingroup$
The set
$$ {(x_n): x_n in {0,1} quad forall n in mathbb N}$$
is uncountable.
answered Jan 14 at 12:55
FredFred
48.7k11849
$endgroup$
add a comment |
$begingroup$
The set
$$ {(x_n): x_n in {0,1} quad forall n in mathbb N}$$
is uncountable.
answered Jan 14 at 12:55
FredFred
48.7k11849
$endgroup$
add a comment |
$begingroup$
The set
$$ {(x_n): x_n in {0,1} quad forall n in mathbb N}$$
is uncountable.
answered Jan 14 at 12:55
FredFred
48.7k11849
$endgroup$
The set
$$ {(x_n): x_n in {0,1} quad forall n in mathbb N}$$
is uncountable.
answered Jan 14 at 12:55
FredFred
48.7k11849
answered Jan 14 at 12:55
FredFred
48.7k11849
answered Jan 14 at 12:55
FredFred
48.7k11849
answered Jan 14 at 12:55
FredFred
48.7k11849
48.7k11849
add a comment |
add a comment |
$begingroup$
There are many.
The fist one to come to mind is the first uncountable ordinal. It is so unrelated to the real numbers that trying to come up with a useful relationship at all between the two was allegedly what drove Georg Cantor mad. There are, of course, any ordinal above that one as well.
As mentioned in the comments, the power-set of any infinite set is uncountably infinite.
answered Jan 14 at 12:50
ArthurArthur
119k7119202
$endgroup$
add a comment |
$begingroup$
There are many.
The fist one to come to mind is the first uncountable ordinal. It is so unrelated to the real numbers that trying to come up with a useful relationship at all between the two was allegedly what drove Georg Cantor mad. There are, of course, any ordinal above that one as well.
As mentioned in the comments, the power-set of any infinite set is uncountably infinite.
answered Jan 14 at 12:50
ArthurArthur
119k7119202
$endgroup$
add a comment |
$begingroup$
There are many.
The fist one to come to mind is the first uncountable ordinal. It is so unrelated to the real numbers that trying to come up with a useful relationship at all between the two was allegedly what drove Georg Cantor mad. There are, of course, any ordinal above that one as well.
As mentioned in the comments, the power-set of any infinite set is uncountably infinite.
answered Jan 14 at 12:50
ArthurArthur
119k7119202
$endgroup$
There are many.
The fist one to come to mind is the first uncountable ordinal. It is so unrelated to the real numbers that trying to come up with a useful relationship at all between the two was allegedly what drove Georg Cantor mad. There are, of course, any ordinal above that one as well.
As mentioned in the comments, the power-set of any infinite set is uncountably infinite.
answered Jan 14 at 12:50
ArthurArthur
119k7119202
answered Jan 14 at 12:50
ArthurArthur
119k7119202
answered Jan 14 at 12:50
ArthurArthur
119k7119202
answered Jan 14 at 12:50
ArthurArthur
119k7119202
119k7119202
add a comment |
add a comment |
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1
$begingroup$
The set of subsets (i.e. power-set) of every countable infinite set.
$endgroup$
– Mauro ALLEGRANZA
Jan 14 at 12:47
1
$begingroup$
The set of all functions from $mathbb{N}tomathbb{N}$ is always an interesting example.
$endgroup$
– user3482749
Jan 14 at 12:48
1
$begingroup$
I like the first uncountable ordinal
$endgroup$
– Questioner
Jan 14 at 13:52