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Something confusing in the proof of existence of simple sets in Soarse's book. [closed]
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In Soares's book he tries to prove that there's a simple set and I understand it well but there's something confuses me when he proves that the complement of $A$ is infinite he says that $mathrmcard(textcomplement of $A$ restricted to $2e$)ge e+1$ therefore the complement of $A$ is infinite!!!!!
Or $A$ intersection $[0, 2i) le i$ then the complement of $A$ is infinite!!
I cant figure out why it's infinite???
It's so confusing to me.
Please help if you can.
Thanks!
computability
asked Jul 24 at 14:01
Student
192
closed as off-topic by M. Winter, Xander Henderson, Shailesh, Lord Shark the Unknown, rtybase Jul 26 at 19:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – M. Winter, Xander Henderson, Shailesh
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up vote
2
down vote
favorite
In Soares's book he tries to prove that there's a simple set and I understand it well but there's something confuses me when he proves that the complement of $A$ is infinite he says that $mathrmcard(textcomplement of $A$ restricted to $2e$)ge e+1$ therefore the complement of $A$ is infinite!!!!!
Or $A$ intersection $[0, 2i) le i$ then the complement of $A$ is infinite!!
I cant figure out why it's infinite???
It's so confusing to me.
Please help if you can.
Thanks!
computability
asked Jul 24 at 14:01
Student
192
closed as off-topic by M. Winter, Xander Henderson, Shailesh, Lord Shark the Unknown, rtybase Jul 26 at 19:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – M. Winter, Xander Henderson, Shailesh
What is a simple set?
– M. Winter
Jul 24 at 14:03
What is $A$ restricted to $2e?$ Please use MathJax to format questions on this site.
– saulspatz
Jul 24 at 14:19
Think about what happens as $e$ goes to infinity (or as $i$ goes to infinity) ...
– Noah Schweber
Jul 25 at 1:48
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
In Soares's book he tries to prove that there's a simple set and I understand it well but there's something confuses me when he proves that the complement of $A$ is infinite he says that $mathrmcard(textcomplement of $A$ restricted to $2e$)ge e+1$ therefore the complement of $A$ is infinite!!!!!
Or $A$ intersection $[0, 2i) le i$ then the complement of $A$ is infinite!!
I cant figure out why it's infinite???
It's so confusing to me.
Please help if you can.
Thanks!
computability
asked Jul 24 at 14:01
Student
192
In Soares's book he tries to prove that there's a simple set and I understand it well but there's something confuses me when he proves that the complement of $A$ is infinite he says that $mathrmcard(textcomplement of $A$ restricted to $2e$)ge e+1$ therefore the complement of $A$ is infinite!!!!!
Or $A$ intersection $[0, 2i) le i$ then the complement of $A$ is infinite!!
I cant figure out why it's infinite???
It's so confusing to me.
Please help if you can.
Thanks!
computability
asked Jul 24 at 14:01
Student
192
edited Jul 24 at 14:14
asked Jul 24 at 14:01
Student
192
asked Jul 24 at 14:01
Student
192
asked Jul 24 at 14:01
Student
192
192
closed as off-topic by M. Winter, Xander Henderson, Shailesh, Lord Shark the Unknown, rtybase Jul 26 at 19:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – M. Winter, Xander Henderson, Shailesh
closed as off-topic by M. Winter, Xander Henderson, Shailesh, Lord Shark the Unknown, rtybase Jul 26 at 19:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – M. Winter, Xander Henderson, Shailesh
What is a simple set?
– M. Winter
Jul 24 at 14:03
What is $A$ restricted to $2e?$ Please use MathJax to format questions on this site.
– saulspatz
Jul 24 at 14:19
Think about what happens as $e$ goes to infinity (or as $i$ goes to infinity) ...
– Noah Schweber
Jul 25 at 1:48
add a comment |Â
What is a simple set?
– M. Winter
Jul 24 at 14:03
What is $A$ restricted to $2e?$ Please use MathJax to format questions on this site.
– saulspatz
Jul 24 at 14:19
Think about what happens as $e$ goes to infinity (or as $i$ goes to infinity) ...
– Noah Schweber
Jul 25 at 1:48
What is a simple set?
– M. Winter
Jul 24 at 14:03
What is a simple set?
– M. Winter
Jul 24 at 14:03
What is $A$ restricted to $2e?$ Please use MathJax to format questions on this site.
– saulspatz
Jul 24 at 14:19
What is $A$ restricted to $2e?$ Please use MathJax to format questions on this site.
– saulspatz
Jul 24 at 14:19
Think about what happens as $e$ goes to infinity (or as $i$ goes to infinity) ...
– Noah Schweber
Jul 25 at 1:48
Think about what happens as $e$ goes to infinity (or as $i$ goes to infinity) ...
– Noah Schweber
Jul 25 at 1:48
add a comment |Â
1 Answer
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For every $einBbb N$, a subset of $A^complement$ has cardinality $>e$, so $|A^complement|>e$.
answered Jul 24 at 14:25
Berci
56.4k23570
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
For every $einBbb N$, a subset of $A^complement$ has cardinality $>e$, so $|A^complement|>e$.
answered Jul 24 at 14:25
Berci
56.4k23570
add a comment |Â
up vote
0
down vote
For every $einBbb N$, a subset of $A^complement$ has cardinality $>e$, so $|A^complement|>e$.
answered Jul 24 at 14:25
Berci
56.4k23570
add a comment |Â
up vote
0
down vote
up vote
0
down vote
For every $einBbb N$, a subset of $A^complement$ has cardinality $>e$, so $|A^complement|>e$.
answered Jul 24 at 14:25
Berci
56.4k23570
For every $einBbb N$, a subset of $A^complement$ has cardinality $>e$, so $|A^complement|>e$.
answered Jul 24 at 14:25
Berci
56.4k23570
answered Jul 24 at 14:25
Berci
56.4k23570
answered Jul 24 at 14:25
Berci
56.4k23570
answered Jul 24 at 14:25
Berci
56.4k23570
56.4k23570
add a comment |Â
add a comment |Â
What is a simple set?
– M. Winter
Jul 24 at 14:03
What is $A$ restricted to $2e?$ Please use MathJax to format questions on this site.
– saulspatz
Jul 24 at 14:19
Think about what happens as $e$ goes to infinity (or as $i$ goes to infinity) ...
– Noah Schweber
Jul 25 at 1:48