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. Ford
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asked Jan 7 at 20:16
user626365user626365
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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. Ford
451111
asked Jan 7 at 20:16
user626365user626365
61
New contributor
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Check out our Code of Conduct.
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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.
$begingroup$
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. Ford
451111
asked Jan 7 at 20:16
user626365user626365
61
New contributor
user626365 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
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. Ford
451111
asked Jan 7 at 20:16
user626365user626365
61
New contributor
user626365 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Jan 7 at 21:17
T. Ford
451111
asked Jan 7 at 20:16
user626365user626365
61
New contributor
user626365 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Jan 7 at 21:17
T. Ford
451111
edited Jan 7 at 21:17
T. Ford
451111
edited Jan 7 at 21:17
T. Ford
451111
451111
asked Jan 7 at 20:16
user626365user626365
61
New contributor
user626365 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 7 at 20:16
user626365user626365
61
asked Jan 7 at 20:16
user626365user626365
61
61
New contributor
user626365 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user626365 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user626365 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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
Users with the general-topology badge can single-handedly close general-topology questions as duplicates and reopen them as needed.
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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
$begingroup$
There is no contradiction. Countable infinity is just a special kind of infinity.
answered Jan 7 at 20:28
Math_QEDMath_QED
7,33831450
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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
7,33831450
$endgroup$
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
7,33831450
$endgroup$
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
7,33831450
$endgroup$
There is no contradiction. Countable infinity is just a special kind of infinity.
answered Jan 7 at 20:28
Math_QEDMath_QED
7,33831450
answered Jan 7 at 20:28
Math_QEDMath_QED
7,33831450
answered Jan 7 at 20:28
Math_QEDMath_QED
7,33831450
answered Jan 7 at 20:28
Math_QEDMath_QED
7,33831450
7,33831450
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