Find the set of interstion of $ (mathbb{Z}_p setminus mathbb{Z}) cap mathbb{Q}$ shwoing its elements...
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Is the set $ (mathbb{Z}_p setminus mathbb{Z}) cap mathbb{Q}$ non-empty? [closed]
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This question is from $text{p-adic numbers}.$
My questions are-
$(1)$ Is the set $ (mathbb{Z}_p setminus mathbb{Z}) cap mathbb{Q}$ non-empty? If non-empty, then what are the elements or the intersection set?
$(2)$ Is the set $ (mathbb{Z}_p setminus mathbb{Z}) cap mathbb{Q}_p $ non-empty? If non-empty what are the elements or the intersection set?
I can not conclude the answer.
Please someone help me with details answer or at least hints.
p-adic-number-theory
asked Nov 29 at 4:08
M. A. SARKAR
2,1271619
marked as duplicate by Torsten Schoeneberg, Ali Caglayan, Rebellos, José Carlos Santos, supinf Nov 29 at 14:41
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.
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up vote
1
down vote
favorite
This question already has an answer here:
Is the set $ (mathbb{Z}_p setminus mathbb{Z}) cap mathbb{Q}$ non-empty? [closed]
1 answer
This question is from $text{p-adic numbers}.$
My questions are-
$(1)$ Is the set $ (mathbb{Z}_p setminus mathbb{Z}) cap mathbb{Q}$ non-empty? If non-empty, then what are the elements or the intersection set?
$(2)$ Is the set $ (mathbb{Z}_p setminus mathbb{Z}) cap mathbb{Q}_p $ non-empty? If non-empty what are the elements or the intersection set?
I can not conclude the answer.
Please someone help me with details answer or at least hints.
p-adic-number-theory
asked Nov 29 at 4:08
M. A. SARKAR
2,1271619
marked as duplicate by Torsten Schoeneberg, Ali Caglayan, Rebellos, José Carlos Santos, supinf Nov 29 at 14:41
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 |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
This question already has an answer here:
Is the set $ (mathbb{Z}_p setminus mathbb{Z}) cap mathbb{Q}$ non-empty? [closed]
1 answer
This question is from $text{p-adic numbers}.$
My questions are-
$(1)$ Is the set $ (mathbb{Z}_p setminus mathbb{Z}) cap mathbb{Q}$ non-empty? If non-empty, then what are the elements or the intersection set?
$(2)$ Is the set $ (mathbb{Z}_p setminus mathbb{Z}) cap mathbb{Q}_p $ non-empty? If non-empty what are the elements or the intersection set?
I can not conclude the answer.
Please someone help me with details answer or at least hints.
p-adic-number-theory
asked Nov 29 at 4:08
M. A. SARKAR
2,1271619
This question already has an answer here:
Is the set $ (mathbb{Z}_p setminus mathbb{Z}) cap mathbb{Q}$ non-empty? [closed]
1 answer
This question is from $text{p-adic numbers}.$
My questions are-
$(1)$ Is the set $ (mathbb{Z}_p setminus mathbb{Z}) cap mathbb{Q}$ non-empty? If non-empty, then what are the elements or the intersection set?
$(2)$ Is the set $ (mathbb{Z}_p setminus mathbb{Z}) cap mathbb{Q}_p $ non-empty? If non-empty what are the elements or the intersection set?
I can not conclude the answer.
Please someone help me with details answer or at least hints.
This question already has an answer here:
Is the set $ (mathbb{Z}_p setminus mathbb{Z}) cap mathbb{Q}$ non-empty? [closed]
1 answer
p-adic-number-theory
p-adic-number-theory
asked Nov 29 at 4:08
M. A. SARKAR
2,1271619
asked Nov 29 at 4:08
M. A. SARKAR
2,1271619
asked Nov 29 at 4:08
M. A. SARKAR
2,1271619
asked Nov 29 at 4:08
M. A. SARKAR
2,1271619
asked Nov 29 at 4:08
M. A. SARKAR
2,1271619
2,1271619
marked as duplicate by Torsten Schoeneberg, Ali Caglayan, Rebellos, José Carlos Santos, supinf Nov 29 at 14:41
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 Torsten Schoeneberg, Ali Caglayan, Rebellos, José Carlos Santos, supinf Nov 29 at 14:41
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 |
add a comment |
1 Answer
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Hint: $frac{1}{2} in mathbb{Z}_3 setminus mathbb{Z}$, since $$frac{1}{2}= frac{-1}{1-3} = -1-3-9-27- dots.$$ That (1) is nonempty implies that (2) is.
Similarly, you can prove that any $frac{a}{b} in mathbb{Z}_3 setminus mathbb{Z}$ so long $3 nmid b.$
answered Nov 29 at 4:15
Dzoooks
846316
yes that is one element and so non-empty.. But I need to find the whole and general expression of the intersection set .. Can you do that that for general $p$?
– M. A. SARKAR
Nov 29 at 4:17
Simply inductive construct the inverse power series of $b$ for $frac{1}{b}.$
– Dzoooks
Nov 29 at 4:19
Does $ frac{a}{b} in mathbb{Q}_p$?
– M. A. SARKAR
Nov 29 at 4:19
1
Yes. $mathbb{Q}_p supset mathbb{Q}$.
– Dzoooks
Nov 29 at 4:20
1
Asking someone to put an answer in that special form sounds like you are asking someone to provide the answer to a homework question. That is not a reasonable request.
– KCd
Nov 29 at 6:28
|
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Hint: $frac{1}{2} in mathbb{Z}_3 setminus mathbb{Z}$, since $$frac{1}{2}= frac{-1}{1-3} = -1-3-9-27- dots.$$ That (1) is nonempty implies that (2) is.
Similarly, you can prove that any $frac{a}{b} in mathbb{Z}_3 setminus mathbb{Z}$ so long $3 nmid b.$
answered Nov 29 at 4:15
Dzoooks
846316
yes that is one element and so non-empty.. But I need to find the whole and general expression of the intersection set .. Can you do that that for general $p$?
– M. A. SARKAR
Nov 29 at 4:17
Simply inductive construct the inverse power series of $b$ for $frac{1}{b}.$
– Dzoooks
Nov 29 at 4:19
Does $ frac{a}{b} in mathbb{Q}_p$?
– M. A. SARKAR
Nov 29 at 4:19
1
Yes. $mathbb{Q}_p supset mathbb{Q}$.
– Dzoooks
Nov 29 at 4:20
1
Asking someone to put an answer in that special form sounds like you are asking someone to provide the answer to a homework question. That is not a reasonable request.
– KCd
Nov 29 at 6:28
|
show 1 more comment
up vote
1
down vote
Hint: $frac{1}{2} in mathbb{Z}_3 setminus mathbb{Z}$, since $$frac{1}{2}= frac{-1}{1-3} = -1-3-9-27- dots.$$ That (1) is nonempty implies that (2) is.
Similarly, you can prove that any $frac{a}{b} in mathbb{Z}_3 setminus mathbb{Z}$ so long $3 nmid b.$
answered Nov 29 at 4:15
Dzoooks
846316
yes that is one element and so non-empty.. But I need to find the whole and general expression of the intersection set .. Can you do that that for general $p$?
– M. A. SARKAR
Nov 29 at 4:17
Simply inductive construct the inverse power series of $b$ for $frac{1}{b}.$
– Dzoooks
Nov 29 at 4:19
Does $ frac{a}{b} in mathbb{Q}_p$?
– M. A. SARKAR
Nov 29 at 4:19
1
Yes. $mathbb{Q}_p supset mathbb{Q}$.
– Dzoooks
Nov 29 at 4:20
1
Asking someone to put an answer in that special form sounds like you are asking someone to provide the answer to a homework question. That is not a reasonable request.
– KCd
Nov 29 at 6:28
|
show 1 more comment
up vote
1
down vote
up vote
1
down vote
Hint: $frac{1}{2} in mathbb{Z}_3 setminus mathbb{Z}$, since $$frac{1}{2}= frac{-1}{1-3} = -1-3-9-27- dots.$$ That (1) is nonempty implies that (2) is.
Similarly, you can prove that any $frac{a}{b} in mathbb{Z}_3 setminus mathbb{Z}$ so long $3 nmid b.$
answered Nov 29 at 4:15
Dzoooks
846316
Hint: $frac{1}{2} in mathbb{Z}_3 setminus mathbb{Z}$, since $$frac{1}{2}= frac{-1}{1-3} = -1-3-9-27- dots.$$ That (1) is nonempty implies that (2) is.
Similarly, you can prove that any $frac{a}{b} in mathbb{Z}_3 setminus mathbb{Z}$ so long $3 nmid b.$
answered Nov 29 at 4:15
Dzoooks
846316
edited Nov 29 at 4:17
answered Nov 29 at 4:15
Dzoooks
846316
answered Nov 29 at 4:15
Dzoooks
846316
answered Nov 29 at 4:15
Dzoooks
846316
846316
yes that is one element and so non-empty.. But I need to find the whole and general expression of the intersection set .. Can you do that that for general $p$?
– M. A. SARKAR
Nov 29 at 4:17
Simply inductive construct the inverse power series of $b$ for $frac{1}{b}.$
– Dzoooks
Nov 29 at 4:19
Does $ frac{a}{b} in mathbb{Q}_p$?
– M. A. SARKAR
Nov 29 at 4:19
1
Yes. $mathbb{Q}_p supset mathbb{Q}$.
– Dzoooks
Nov 29 at 4:20
1
Asking someone to put an answer in that special form sounds like you are asking someone to provide the answer to a homework question. That is not a reasonable request.
– KCd
Nov 29 at 6:28
|
show 1 more comment
yes that is one element and so non-empty.. But I need to find the whole and general expression of the intersection set .. Can you do that that for general $p$?
– M. A. SARKAR
Nov 29 at 4:17
Simply inductive construct the inverse power series of $b$ for $frac{1}{b}.$
– Dzoooks
Nov 29 at 4:19
Does $ frac{a}{b} in mathbb{Q}_p$?
– M. A. SARKAR
Nov 29 at 4:19
1
Yes. $mathbb{Q}_p supset mathbb{Q}$.
– Dzoooks
Nov 29 at 4:20
1
Asking someone to put an answer in that special form sounds like you are asking someone to provide the answer to a homework question. That is not a reasonable request.
– KCd
Nov 29 at 6:28
yes that is one element and so non-empty.. But I need to find the whole and general expression of the intersection set .. Can you do that that for general $p$?
– M. A. SARKAR
Nov 29 at 4:17
yes that is one element and so non-empty.. But I need to find the whole and general expression of the intersection set .. Can you do that that for general $p$?
– M. A. SARKAR
Nov 29 at 4:17
Simply inductive construct the inverse power series of $b$ for $frac{1}{b}.$
– Dzoooks
Nov 29 at 4:19
Simply inductive construct the inverse power series of $b$ for $frac{1}{b}.$
– Dzoooks
Nov 29 at 4:19
Does $ frac{a}{b} in mathbb{Q}_p$?
– M. A. SARKAR
Nov 29 at 4:19
Does $ frac{a}{b} in mathbb{Q}_p$?
– M. A. SARKAR
Nov 29 at 4:19
1
1
Yes. $mathbb{Q}_p supset mathbb{Q}$.
– Dzoooks
Nov 29 at 4:20
Yes. $mathbb{Q}_p supset mathbb{Q}$.
– Dzoooks
Nov 29 at 4:20
1
1
Asking someone to put an answer in that special form sounds like you are asking someone to provide the answer to a homework question. That is not a reasonable request.
– KCd
Nov 29 at 6:28
Asking someone to put an answer in that special form sounds like you are asking someone to provide the answer to a homework question. That is not a reasonable request.
– KCd
Nov 29 at 6:28
|
show 1 more comment
