Mixing
Real analysis, topology [duplicate]
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This question already has an answer here:
If A is infinite, does there have to exist a subset of A that is equivalent to A?
2 answers
"If a set is equivalent to one of its proper subset then it is infinite set"
I was wondering why can't it be countably infinite? Since $mathbb{Z} sim mathbb{N} sim mathbb{Z}+ rightarrow mathbb{Z}+ sim mathbb{Z}$, $mathbb{Z}$ is countably infinite hence $mathbb{Z}$ is equivalent to its proper subset but Z is countably infinite.. Please correct me where I am getting it wrong
real-analysis general-topology
edited Jan 7 at 21:17
T. Fo
476311
asked Jan 7 at 20:16
user626365user626365
111
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marked as duplicate by Dietrich Burde, KReiser, mrtaurho, Lord Shark the Unknown, José Carlos Santos general-topology
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Jan 8 at 10:57
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
1
$begingroup$
This question already has an answer here:
If A is infinite, does there have to exist a subset of A that is equivalent to A?
2 answers
"If a set is equivalent to one of its proper subset then it is infinite set"
I was wondering why can't it be countably infinite? Since $mathbb{Z} sim mathbb{N} sim mathbb{Z}+ rightarrow mathbb{Z}+ sim mathbb{Z}$, $mathbb{Z}$ is countably infinite hence $mathbb{Z}$ is equivalent to its proper subset but Z is countably infinite.. Please correct me where I am getting it wrong
real-analysis general-topology
edited Jan 7 at 21:17
T. Fo
476311
asked Jan 7 at 20:16
user626365user626365
111
$endgroup$
marked as duplicate by Dietrich Burde, KReiser, mrtaurho, Lord Shark the Unknown, José Carlos Santos general-topology
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Jan 8 at 10:57
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
Welcome to Math.SE! Please use MathJax. For some basic information about writing math at this site see e.g. basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
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– GNUSupporter 8964民主女神 地下教會
Jan 7 at 20:17
6
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Countably infinite is infinite.
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– Mindlack
Jan 7 at 20:17
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Hello, you seem to have confused the title field for the tags field. You should think about making your title informative about the question you are asking. I've taken the liberty of providing a better title. Please do something similar in the future.
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– rschwieb
Jan 7 at 20:18
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It always is true, assuming the axiom of choice, see this duplicate: A set is infinite if it is equivalent to one of its subsets.
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– Dietrich Burde
Jan 7 at 20:19
add a comment |
1
1
1
$begingroup$
This question already has an answer here:
If A is infinite, does there have to exist a subset of A that is equivalent to A?
2 answers
"If a set is equivalent to one of its proper subset then it is infinite set"
I was wondering why can't it be countably infinite? Since $mathbb{Z} sim mathbb{N} sim mathbb{Z}+ rightarrow mathbb{Z}+ sim mathbb{Z}$, $mathbb{Z}$ is countably infinite hence $mathbb{Z}$ is equivalent to its proper subset but Z is countably infinite.. Please correct me where I am getting it wrong
real-analysis general-topology
edited Jan 7 at 21:17
T. Fo
476311
asked Jan 7 at 20:16
user626365user626365
111
$endgroup$
This question already has an answer here:
If A is infinite, does there have to exist a subset of A that is equivalent to A?
2 answers
"If a set is equivalent to one of its proper subset then it is infinite set"
I was wondering why can't it be countably infinite? Since $mathbb{Z} sim mathbb{N} sim mathbb{Z}+ rightarrow mathbb{Z}+ sim mathbb{Z}$, $mathbb{Z}$ is countably infinite hence $mathbb{Z}$ is equivalent to its proper subset but Z is countably infinite.. Please correct me where I am getting it wrong
This question already has an answer here:
If A is infinite, does there have to exist a subset of A that is equivalent to A?
2 answers
real-analysis general-topology
real-analysis general-topology
edited Jan 7 at 21:17
T. Fo
476311
asked Jan 7 at 20:16
user626365user626365
111
edited Jan 7 at 21:17
T. Fo
476311
asked Jan 7 at 20:16
user626365user626365
111
edited Jan 7 at 21:17
T. Fo
476311
edited Jan 7 at 21:17
T. Fo
476311
edited Jan 7 at 21:17
T. Fo
476311
476311
asked Jan 7 at 20:16
user626365user626365
111
asked Jan 7 at 20:16
user626365user626365
111
asked Jan 7 at 20:16
user626365user626365
111
111
marked as duplicate by Dietrich Burde, KReiser, mrtaurho, Lord Shark the Unknown, José Carlos Santos general-topology
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Jan 8 at 10:57
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Dietrich Burde, KReiser, mrtaurho, Lord Shark the Unknown, José Carlos Santos general-topology
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Jan 8 at 10:57
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
Welcome to Math.SE! Please use MathJax. For some basic information about writing math at this site see e.g. basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 7 at 20:17
6
$begingroup$
Countably infinite is infinite.
$endgroup$
– Mindlack
Jan 7 at 20:17
$begingroup$
Hello, you seem to have confused the title field for the tags field. You should think about making your title informative about the question you are asking. I've taken the liberty of providing a better title. Please do something similar in the future.
$endgroup$
– rschwieb
Jan 7 at 20:18
$begingroup$
It always is true, assuming the axiom of choice, see this duplicate: A set is infinite if it is equivalent to one of its subsets.
$endgroup$
– Dietrich Burde
Jan 7 at 20:19
add a comment |
$begingroup$
Welcome to Math.SE! Please use MathJax. For some basic information about writing math at this site see e.g. basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 7 at 20:17
6
$begingroup$
Countably infinite is infinite.
$endgroup$
– Mindlack
Jan 7 at 20:17
$begingroup$
Hello, you seem to have confused the title field for the tags field. You should think about making your title informative about the question you are asking. I've taken the liberty of providing a better title. Please do something similar in the future.
$endgroup$
– rschwieb
Jan 7 at 20:18
$begingroup$
It always is true, assuming the axiom of choice, see this duplicate: A set is infinite if it is equivalent to one of its subsets.
$endgroup$
– Dietrich Burde
Jan 7 at 20:19
$begingroup$
Welcome to Math.SE! Please use MathJax. For some basic information about writing math at this site see e.g. basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 7 at 20:17
$begingroup$
Welcome to Math.SE! Please use MathJax. For some basic information about writing math at this site see e.g. basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 7 at 20:17
6
6
$begingroup$
Countably infinite is infinite.
$endgroup$
– Mindlack
Jan 7 at 20:17
$begingroup$
Countably infinite is infinite.
$endgroup$
– Mindlack
Jan 7 at 20:17
$begingroup$
Hello, you seem to have confused the title field for the tags field. You should think about making your title informative about the question you are asking. I've taken the liberty of providing a better title. Please do something similar in the future.
$endgroup$
– rschwieb
Jan 7 at 20:18
$begingroup$
Hello, you seem to have confused the title field for the tags field. You should think about making your title informative about the question you are asking. I've taken the liberty of providing a better title. Please do something similar in the future.
$endgroup$
– rschwieb
Jan 7 at 20:18
$begingroup$
It always is true, assuming the axiom of choice, see this duplicate: A set is infinite if it is equivalent to one of its subsets.
$endgroup$
– Dietrich Burde
Jan 7 at 20:19
$begingroup$
It always is true, assuming the axiom of choice, see this duplicate: A set is infinite if it is equivalent to one of its subsets.
$endgroup$
– Dietrich Burde
Jan 7 at 20:19
add a comment |
1 Answer
1
active
oldest
votes
4
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There is no contradiction. Countable infinity is just a special kind of infinity.
answered Jan 7 at 20:28
Math_QEDMath_QED
7,52831450
$endgroup$
2
$begingroup$
Thank you .got it!
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– user626365
Jan 7 at 20:37
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You can accept the answer if it helped you. This will gain you (and me as well) rep, which enables perks on the site.
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– Math_QED
Jan 7 at 20:59
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
4
$begingroup$
There is no contradiction. Countable infinity is just a special kind of infinity.
answered Jan 7 at 20:28
Math_QEDMath_QED
7,52831450
$endgroup$
2
$begingroup$
Thank you .got it!
$endgroup$
– user626365
Jan 7 at 20:37
$begingroup$
You can accept the answer if it helped you. This will gain you (and me as well) rep, which enables perks on the site.
$endgroup$
– Math_QED
Jan 7 at 20:59
add a comment |
4
$begingroup$
There is no contradiction. Countable infinity is just a special kind of infinity.
answered Jan 7 at 20:28
Math_QEDMath_QED
7,52831450
$endgroup$
2
$begingroup$
Thank you .got it!
$endgroup$
– user626365
Jan 7 at 20:37
$begingroup$
You can accept the answer if it helped you. This will gain you (and me as well) rep, which enables perks on the site.
$endgroup$
– Math_QED
Jan 7 at 20:59
add a comment |
4
4
4
$begingroup$
There is no contradiction. Countable infinity is just a special kind of infinity.
answered Jan 7 at 20:28
Math_QEDMath_QED
7,52831450
$endgroup$
There is no contradiction. Countable infinity is just a special kind of infinity.
answered Jan 7 at 20:28
Math_QEDMath_QED
7,52831450
answered Jan 7 at 20:28
Math_QEDMath_QED
7,52831450
answered Jan 7 at 20:28
Math_QEDMath_QED
7,52831450
answered Jan 7 at 20:28
Math_QEDMath_QED
7,52831450
7,52831450
2
$begingroup$
Thank you .got it!
$endgroup$
– user626365
Jan 7 at 20:37
$begingroup$
You can accept the answer if it helped you. This will gain you (and me as well) rep, which enables perks on the site.
$endgroup$
– Math_QED
Jan 7 at 20:59
add a comment |
2
$begingroup$
Thank you .got it!
$endgroup$
– user626365
Jan 7 at 20:37
$begingroup$
You can accept the answer if it helped you. This will gain you (and me as well) rep, which enables perks on the site.
$endgroup$
– Math_QED
Jan 7 at 20:59
2
2
$begingroup$
Thank you .got it!
$endgroup$
– user626365
Jan 7 at 20:37
$begingroup$
Thank you .got it!
$endgroup$
– user626365
Jan 7 at 20:37
$begingroup$
You can accept the answer if it helped you. This will gain you (and me as well) rep, which enables perks on the site.
$endgroup$
– Math_QED
Jan 7 at 20:59
$begingroup$
You can accept the answer if it helped you. This will gain you (and me as well) rep, which enables perks on the site.
$endgroup$
– Math_QED
Jan 7 at 20:59
add a comment |
$begingroup$
Welcome to Math.SE! Please use MathJax. For some basic information about writing math at this site see e.g. basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 7 at 20:17
6
$begingroup$
Countably infinite is infinite.
$endgroup$
– Mindlack
Jan 7 at 20:17
$begingroup$
Hello, you seem to have confused the title field for the tags field. You should think about making your title informative about the question you are asking. I've taken the liberty of providing a better title. Please do something similar in the future.
$endgroup$
– rschwieb
Jan 7 at 20:18
$begingroup$
It always is true, assuming the axiom of choice, see this duplicate: A set is infinite if it is equivalent to one of its subsets.
$endgroup$
– Dietrich Burde
Jan 7 at 20:19