How can I write set of all positive rational numbers
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How to write the set of all rational numbers?? From Cantor's matrix we can get the positive ones. Should I add corresponding negative values and a 0?
cantor-set
asked Jan 12 at 23:30
Nilanjasa KunduNilanjasa Kundu
1
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add a comment |
$begingroup$
How to write the set of all rational numbers?? From Cantor's matrix we can get the positive ones. Should I add corresponding negative values and a 0?
cantor-set
asked Jan 12 at 23:30
Nilanjasa KunduNilanjasa Kundu
1
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$begingroup$
Very similarly to the proof showing that all integers are countable.
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– Viktor Glombik
Jan 12 at 23:32
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Yes. After writing the rational number set then I can proof by one to one correspondence that rational numbers are countable. I was confused about the set of rational numbers
$endgroup$
– Nilanjasa Kundu
Jan 13 at 7:42
add a comment |
$begingroup$
How to write the set of all rational numbers?? From Cantor's matrix we can get the positive ones. Should I add corresponding negative values and a 0?
cantor-set
asked Jan 12 at 23:30
Nilanjasa KunduNilanjasa Kundu
1
$endgroup$
How to write the set of all rational numbers?? From Cantor's matrix we can get the positive ones. Should I add corresponding negative values and a 0?
cantor-set
cantor-set
asked Jan 12 at 23:30
Nilanjasa KunduNilanjasa Kundu
1
asked Jan 12 at 23:30
Nilanjasa KunduNilanjasa Kundu
1
asked Jan 12 at 23:30
Nilanjasa KunduNilanjasa Kundu
1
asked Jan 12 at 23:30
Nilanjasa KunduNilanjasa Kundu
1
asked Jan 12 at 23:30
Nilanjasa KunduNilanjasa Kundu
1
1
$begingroup$
Very similarly to the proof showing that all integers are countable.
$endgroup$
– Viktor Glombik
Jan 12 at 23:32
$begingroup$
Yes. After writing the rational number set then I can proof by one to one correspondence that rational numbers are countable. I was confused about the set of rational numbers
$endgroup$
– Nilanjasa Kundu
Jan 13 at 7:42
add a comment |
$begingroup$
Very similarly to the proof showing that all integers are countable.
$endgroup$
– Viktor Glombik
Jan 12 at 23:32
$begingroup$
Yes. After writing the rational number set then I can proof by one to one correspondence that rational numbers are countable. I was confused about the set of rational numbers
$endgroup$
– Nilanjasa Kundu
Jan 13 at 7:42
$begingroup$
Very similarly to the proof showing that all integers are countable.
$endgroup$
– Viktor Glombik
Jan 12 at 23:32
$begingroup$
Very similarly to the proof showing that all integers are countable.
$endgroup$
– Viktor Glombik
Jan 12 at 23:32
$begingroup$
Yes. After writing the rational number set then I can proof by one to one correspondence that rational numbers are countable. I was confused about the set of rational numbers
$endgroup$
– Nilanjasa Kundu
Jan 13 at 7:42
$begingroup$
Yes. After writing the rational number set then I can proof by one to one correspondence that rational numbers are countable. I was confused about the set of rational numbers
$endgroup$
– Nilanjasa Kundu
Jan 13 at 7:42
add a comment |
1 Answer
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Use the order 0,1,-1, 2, -2, 3, -3, ... for the numerator and then apply the Cantor matrix. The denominator can be called positive wlog.
answered Jan 13 at 0:19
Oscar LanziOscar Lanzi
13.7k12136
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1 Answer
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$begingroup$
Use the order 0,1,-1, 2, -2, 3, -3, ... for the numerator and then apply the Cantor matrix. The denominator can be called positive wlog.
answered Jan 13 at 0:19
Oscar LanziOscar Lanzi
13.7k12136
$endgroup$
add a comment |
$begingroup$
Use the order 0,1,-1, 2, -2, 3, -3, ... for the numerator and then apply the Cantor matrix. The denominator can be called positive wlog.
answered Jan 13 at 0:19
Oscar LanziOscar Lanzi
13.7k12136
$endgroup$
add a comment |
$begingroup$
Use the order 0,1,-1, 2, -2, 3, -3, ... for the numerator and then apply the Cantor matrix. The denominator can be called positive wlog.
answered Jan 13 at 0:19
Oscar LanziOscar Lanzi
13.7k12136
$endgroup$
Use the order 0,1,-1, 2, -2, 3, -3, ... for the numerator and then apply the Cantor matrix. The denominator can be called positive wlog.
answered Jan 13 at 0:19
Oscar LanziOscar Lanzi
13.7k12136
answered Jan 13 at 0:19
Oscar LanziOscar Lanzi
13.7k12136
answered Jan 13 at 0:19
Oscar LanziOscar Lanzi
13.7k12136
answered Jan 13 at 0:19
Oscar LanziOscar Lanzi
13.7k12136
13.7k12136
add a comment |
add a comment |
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$begingroup$
Very similarly to the proof showing that all integers are countable.
$endgroup$
– Viktor Glombik
Jan 12 at 23:32
$begingroup$
Yes. After writing the rational number set then I can proof by one to one correspondence that rational numbers are countable. I was confused about the set of rational numbers
$endgroup$
– Nilanjasa Kundu
Jan 13 at 7:42