How to formalize the following statement: “for all integers, n, n^2 is even.” [on hold]

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I am trying to formalize the statement "for all integers $n$, $n^2$ is even" by using mathematical quantifiers but I am not sure if I am on the right track.
I'd be grateful if someone could shed light on it.

calculus

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edited Aug 4 at 1:49

Hans Hüttel

3,0142819

asked Aug 4 at 1:39

Susan mohammad.k

31

put on hold as off-topic by M. Winter, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos 2 days ago

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, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  6
  

  
  
  
  
  
  

  
  $forall nin mathbbN, exists kin mathbbN | n^2=2k$ (note that this statement is false: $3^2=9$).
  – Suzet
  Aug 4 at 1:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I would recommend that you always include what you already have worked out yourself, or you face the danger that your question becomes closed.
  – M. Winter
  Aug 4 at 2:25
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

I am trying to formalize the statement "for all integers $n$, $n^2$ is even" by using mathematical quantifiers but I am not sure if I am on the right track.
I'd be grateful if someone could shed light on it.

calculus

share|cite|improve this question

edited Aug 4 at 1:49

Hans Hüttel

3,0142819

asked Aug 4 at 1:39

Susan mohammad.k

31

put on hold as off-topic by M. Winter, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos 2 days ago

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, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  6
  

  
  
  
  
  
  

  
  $forall nin mathbbN, exists kin mathbbN | n^2=2k$ (note that this statement is false: $3^2=9$).
  – Suzet
  Aug 4 at 1:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I would recommend that you always include what you already have worked out yourself, or you face the danger that your question becomes closed.
  – M. Winter
  Aug 4 at 2:25
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

I am trying to formalize the statement "for all integers $n$, $n^2$ is even" by using mathematical quantifiers but I am not sure if I am on the right track.
I'd be grateful if someone could shed light on it.

calculus

share|cite|improve this question

edited Aug 4 at 1:49

Hans Hüttel

3,0142819

asked Aug 4 at 1:39

Susan mohammad.k

31

I am trying to formalize the statement "for all integers $n$, $n^2$ is even" by using mathematical quantifiers but I am not sure if I am on the right track.
I'd be grateful if someone could shed light on it.

calculus

share|cite|improve this question

edited Aug 4 at 1:49

Hans Hüttel

3,0142819

asked Aug 4 at 1:39

Susan mohammad.k

31

share|cite|improve this question

share|cite|improve this question

edited Aug 4 at 1:49

Hans Hüttel

3,0142819

edited Aug 4 at 1:49

Hans Hüttel

3,0142819

edited Aug 4 at 1:49

Hans Hüttel

3,0142819

3,0142819

asked Aug 4 at 1:39

Susan mohammad.k

31

asked Aug 4 at 1:39

Susan mohammad.k

31

asked Aug 4 at 1:39

Susan mohammad.k

31

31

put on hold as off-topic by M. Winter, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos 2 days ago

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, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos

If this question can be reworded to fit the rules in the help center, please edit the question.

put on hold as off-topic by M. Winter, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos 2 days ago

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, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  6
  

  
  
  
  
  
  

  
  $forall nin mathbbN, exists kin mathbbN | n^2=2k$ (note that this statement is false: $3^2=9$).
  – Suzet
  Aug 4 at 1:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I would recommend that you always include what you already have worked out yourself, or you face the danger that your question becomes closed.
  – M. Winter
  Aug 4 at 2:25
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  6
  

  
  
  
  
  
  

  
  $forall nin mathbbN, exists kin mathbbN | n^2=2k$ (note that this statement is false: $3^2=9$).
  – Suzet
  Aug 4 at 1:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I would recommend that you always include what you already have worked out yourself, or you face the danger that your question becomes closed.
  – M. Winter
  Aug 4 at 2:25
  

  
  
  
  

6

6

$forall nin mathbbN, exists kin mathbbN | n^2=2k$ (note that this statement is false: $3^2=9$).
– Suzet
Aug 4 at 1:41

$forall nin mathbbN, exists kin mathbbN | n^2=2k$ (note that this statement is false: $3^2=9$).
– Suzet
Aug 4 at 1:41

I would recommend that you always include what you already have worked out yourself, or you face the danger that your question becomes closed.
– M. Winter
Aug 4 at 2:25

I would recommend that you always include what you already have worked out yourself, or you face the danger that your question becomes closed.
– M. Winter
Aug 4 at 2:25

add a comment | 

1 Answer
1

active

oldest

votes

up vote
1
down vote



accepted

Note that $mathbbN$ stands for natural numbers.

Since you want to state for all integers, you need to modify $$forall nin mathbbN, exists kin mathbbN | n^2=2k$$ to

$$forall nin mathbbZ, exists kin mathbbZ | n^2=2k$$

share|cite|improve this answer

answered Aug 4 at 2:23

Mohammad Riazi-Kermani

27k41850

add a comment | 

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote



accepted

Note that $mathbbN$ stands for natural numbers.

Since you want to state for all integers, you need to modify $$forall nin mathbbN, exists kin mathbbN | n^2=2k$$ to

$$forall nin mathbbZ, exists kin mathbbZ | n^2=2k$$

share|cite|improve this answer

answered Aug 4 at 2:23

Mohammad Riazi-Kermani

27k41850

add a comment | 

up vote
1
down vote



accepted

Note that $mathbbN$ stands for natural numbers.

Since you want to state for all integers, you need to modify $$forall nin mathbbN, exists kin mathbbN | n^2=2k$$ to

$$forall nin mathbbZ, exists kin mathbbZ | n^2=2k$$

share|cite|improve this answer

answered Aug 4 at 2:23

Mohammad Riazi-Kermani

27k41850

add a comment | 

up vote
1
down vote



accepted

up vote
1
down vote



accepted

Note that $mathbbN$ stands for natural numbers.

Since you want to state for all integers, you need to modify $$forall nin mathbbN, exists kin mathbbN | n^2=2k$$ to

$$forall nin mathbbZ, exists kin mathbbZ | n^2=2k$$

share|cite|improve this answer

answered Aug 4 at 2:23

Mohammad Riazi-Kermani

27k41850

Note that $mathbbN$ stands for natural numbers.

Since you want to state for all integers, you need to modify $$forall nin mathbbN, exists kin mathbbN | n^2=2k$$ to

$$forall nin mathbbZ, exists kin mathbbZ | n^2=2k$$

share|cite|improve this answer

answered Aug 4 at 2:23

Mohammad Riazi-Kermani

27k41850

share|cite|improve this answer

share|cite|improve this answer

answered Aug 4 at 2:23

Mohammad Riazi-Kermani

27k41850

answered Aug 4 at 2:23

Mohammad Riazi-Kermani

27k41850

answered Aug 4 at 2:23

Mohammad Riazi-Kermani

27k41850

27k41850

add a comment | 

add a comment |