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Good notation to require that z ≠ 0, -1, -2, -3, …

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2

0

$begingroup$

An engineer in my 50s, I have gradually been trying to improve my mathematical notation, an effort your answers here at Math.SE have partly inspired. Therefore, if $z in mathbb C$, may I ask whether I have written this in good style? $$z notin {n | n in mathbb Z wedge n le 0}$$ Or is this better? $$z notin {n in mathbb Z | n le 0}$$ Or is this better? $$z notin {n in mathbb Z le 0}$$ Or even this? $$z notin {mathbb Z le 0}$$ Or this? $$z notinmathbb Z le 0$$ Or something else? If you find a flaw in any or all of my notations (and I do not doubt that you will), then would you illuminate my misconception?

The $z$ is an arbitrary complex number except that $z = 0, -1, -2, -3,ldots$ [the poles of $Gamma(z)$] are not allowed.

soft-question notation

share|cite|improve this question

edited 7 hours ago

thb

asked 8 hours ago

thbthb

24711 silver badge1010 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What's wrong with just writing "[$zin mathbb{C}$ with] $znot = 0, -1, -2, dots$"?
  $endgroup$
  – anomaly
  8 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @anomaly Only that I did not know that that is an accepted notation.
  $endgroup$
  – thb
  8 hours ago
  

  
  
  
  

add a comment
 | 

2

0

$begingroup$

An engineer in my 50s, I have gradually been trying to improve my mathematical notation, an effort your answers here at Math.SE have partly inspired. Therefore, if $z in mathbb C$, may I ask whether I have written this in good style? $$z notin {n | n in mathbb Z wedge n le 0}$$ Or is this better? $$z notin {n in mathbb Z | n le 0}$$ Or is this better? $$z notin {n in mathbb Z le 0}$$ Or even this? $$z notin {mathbb Z le 0}$$ Or this? $$z notinmathbb Z le 0$$ Or something else? If you find a flaw in any or all of my notations (and I do not doubt that you will), then would you illuminate my misconception?

The $z$ is an arbitrary complex number except that $z = 0, -1, -2, -3,ldots$ [the poles of $Gamma(z)$] are not allowed.

soft-question notation

share|cite|improve this question

edited 7 hours ago

thb

asked 8 hours ago

thbthb

24711 silver badge1010 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What's wrong with just writing "[$zin mathbb{C}$ with] $znot = 0, -1, -2, dots$"?
  $endgroup$
  – anomaly
  8 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @anomaly Only that I did not know that that is an accepted notation.
  $endgroup$
  – thb
  8 hours ago
  

  
  
  
  

add a comment
 | 

$begingroup$

An engineer in my 50s, I have gradually been trying to improve my mathematical notation, an effort your answers here at Math.SE have partly inspired. Therefore, if $z in mathbb C$, may I ask whether I have written this in good style? $$z notin {n | n in mathbb Z wedge n le 0}$$ Or is this better? $$z notin {n in mathbb Z | n le 0}$$ Or is this better? $$z notin {n in mathbb Z le 0}$$ Or even this? $$z notin {mathbb Z le 0}$$ Or this? $$z notinmathbb Z le 0$$ Or something else? If you find a flaw in any or all of my notations (and I do not doubt that you will), then would you illuminate my misconception?

The $z$ is an arbitrary complex number except that $z = 0, -1, -2, -3,ldots$ [the poles of $Gamma(z)$] are not allowed.

soft-question notation

share|cite|improve this question

edited 7 hours ago

thb

asked 8 hours ago

thbthb

24711 silver badge1010 bronze badges

$endgroup$

share|cite|improve this question

edited 7 hours ago

thb

asked 8 hours ago

thbthb

24711 silver badge1010 bronze badges

share|cite|improve this question

edited 7 hours ago

thb

asked 8 hours ago

thbthb

24711 silver badge1010 bronze badges

asked 8 hours ago

thbthb

24711 silver badge1010 bronze badges

asked 8 hours ago

thbthb

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3 Answers
3

active

oldest

votes

5

$begingroup$

Since $zinmathbb{C}$ we should also provide this information. Complex numbers which are not zero or negative integers are often specified as
begin{align*}
zinmathbb{C}setminus{0,-1,-2,ldots}
end{align*}

share|cite|improve this answer

answered 6 hours ago

Markus ScheuerMarkus Scheuer

68.5k44 gold badges6565 silver badges164164 bronze badges

$endgroup$

add a comment
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2

$begingroup$

Personally, I would say $znotin mathbb{Z}^{leq 0}$.

share|cite|improve this answer

answered 8 hours ago

LaarzLaarz

42122 silver badges1111 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I assume that some of my other notations are overelaborate, awkward and/or wrong. If you elaborated, I would be interested.
  $endgroup$
  – thb
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @thb The second one you gave is the only one that I think I would find in a text. $znotin {nin mathbb{Z}mid nleq 0}$, but this assume that the total domain is $mathbb{Z}$. I now realize you might be talking about the complex plane. In which case, you might write it as, $zin mathbb{C}setminus mathbb{Z}^{leq 0} = {zinmathbb{C}| zne n, nin mathbb{Z}^{leq 0}}$.
  $endgroup$
  – Laarz
  8 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, that is my trouble, isn't it? My notation was poor, so you did not know what I was talking about. I am indeed talking about the complex plane. Your answer shows me how to improve my notation.
  $endgroup$
  – thb
  7 hours ago
  
  
  

  
  
  
  

add a comment
 | 

1

$begingroup$

I don't like any of these. Too much notation makes questions harder to read, and none of these clarify what $z$ is allowed to be. If $z$ (notice! this is a total guess!) is supposed to be a complex number, I would say, "let $z in mathbb{C}$ be a complex number that is not a non-positive integer."

---

Edit: I've just seen that $z$ is supposed to be an integer. In this case we should just write $z in mathbb{N}$. Most authors define the natural numbers $mathbb{N}$ to be the set of positive integers.

share|cite|improve this answer

edited 8 hours ago

answered 8 hours ago

Rylee LymanRylee Lyman

2,24433 silver badges2020 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, that is how I usually write. Good advice, but today I am explicitly trying to master the formalism. The $z$ is indeed complex: it's the same $z$ that appears in Abramowitz & Stegun.
  $endgroup$
  – thb
  8 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I have edited my question to clarify.
  $endgroup$
  – thb
  8 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  +1 for minimizing notation. If necessary the OP can clarify that $0 notin mathbb{N}$.
  $endgroup$
  – Ethan Bolker
  6 hours ago
  

  
  
  
  

add a comment
 | 

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5

$begingroup$

Since $zinmathbb{C}$ we should also provide this information. Complex numbers which are not zero or negative integers are often specified as
begin{align*}
zinmathbb{C}setminus{0,-1,-2,ldots}
end{align*}

share|cite|improve this answer

answered 6 hours ago

Markus ScheuerMarkus Scheuer

68.5k44 gold badges6565 silver badges164164 bronze badges

$endgroup$

add a comment
 | 

5

$begingroup$

Since $zinmathbb{C}$ we should also provide this information. Complex numbers which are not zero or negative integers are often specified as
begin{align*}
zinmathbb{C}setminus{0,-1,-2,ldots}
end{align*}

share|cite|improve this answer

answered 6 hours ago

Markus ScheuerMarkus Scheuer

68.5k44 gold badges6565 silver badges164164 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

Since $zinmathbb{C}$ we should also provide this information. Complex numbers which are not zero or negative integers are often specified as
begin{align*}
zinmathbb{C}setminus{0,-1,-2,ldots}
end{align*}

share|cite|improve this answer

answered 6 hours ago

Markus ScheuerMarkus Scheuer

68.5k44 gold badges6565 silver badges164164 bronze badges

$endgroup$

share|cite|improve this answer

answered 6 hours ago

Markus ScheuerMarkus Scheuer

68.5k44 gold badges6565 silver badges164164 bronze badges

answered 6 hours ago

Markus ScheuerMarkus Scheuer

68.5k44 gold badges6565 silver badges164164 bronze badges

answered 6 hours ago

Markus ScheuerMarkus Scheuer

68.5k44 gold badges6565 silver badges164164 bronze badges

2

$begingroup$

Personally, I would say $znotin mathbb{Z}^{leq 0}$.

share|cite|improve this answer

answered 8 hours ago

LaarzLaarz

42122 silver badges1111 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I assume that some of my other notations are overelaborate, awkward and/or wrong. If you elaborated, I would be interested.
  $endgroup$
  – thb
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @thb The second one you gave is the only one that I think I would find in a text. $znotin {nin mathbb{Z}mid nleq 0}$, but this assume that the total domain is $mathbb{Z}$. I now realize you might be talking about the complex plane. In which case, you might write it as, $zin mathbb{C}setminus mathbb{Z}^{leq 0} = {zinmathbb{C}| zne n, nin mathbb{Z}^{leq 0}}$.
  $endgroup$
  – Laarz
  8 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, that is my trouble, isn't it? My notation was poor, so you did not know what I was talking about. I am indeed talking about the complex plane. Your answer shows me how to improve my notation.
  $endgroup$
  – thb
  7 hours ago
  
  
  

  
  
  
  

add a comment
 | 

2

$begingroup$

Personally, I would say $znotin mathbb{Z}^{leq 0}$.

share|cite|improve this answer

answered 8 hours ago

LaarzLaarz

42122 silver badges1111 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I assume that some of my other notations are overelaborate, awkward and/or wrong. If you elaborated, I would be interested.
  $endgroup$
  – thb
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @thb The second one you gave is the only one that I think I would find in a text. $znotin {nin mathbb{Z}mid nleq 0}$, but this assume that the total domain is $mathbb{Z}$. I now realize you might be talking about the complex plane. In which case, you might write it as, $zin mathbb{C}setminus mathbb{Z}^{leq 0} = {zinmathbb{C}| zne n, nin mathbb{Z}^{leq 0}}$.
  $endgroup$
  – Laarz
  8 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, that is my trouble, isn't it? My notation was poor, so you did not know what I was talking about. I am indeed talking about the complex plane. Your answer shows me how to improve my notation.
  $endgroup$
  – thb
  7 hours ago
  
  
  

  
  
  
  

add a comment
 | 

$begingroup$

Personally, I would say $znotin mathbb{Z}^{leq 0}$.

share|cite|improve this answer

answered 8 hours ago

LaarzLaarz

42122 silver badges1111 bronze badges

$endgroup$

share|cite|improve this answer

answered 8 hours ago

LaarzLaarz

42122 silver badges1111 bronze badges

answered 8 hours ago

LaarzLaarz

42122 silver badges1111 bronze badges

answered 8 hours ago

LaarzLaarz

42122 silver badges1111 bronze badges

1

$begingroup$

I don't like any of these. Too much notation makes questions harder to read, and none of these clarify what $z$ is allowed to be. If $z$ (notice! this is a total guess!) is supposed to be a complex number, I would say, "let $z in mathbb{C}$ be a complex number that is not a non-positive integer."

---

Edit: I've just seen that $z$ is supposed to be an integer. In this case we should just write $z in mathbb{N}$. Most authors define the natural numbers $mathbb{N}$ to be the set of positive integers.

share|cite|improve this answer

edited 8 hours ago

answered 8 hours ago

Rylee LymanRylee Lyman

2,24433 silver badges2020 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, that is how I usually write. Good advice, but today I am explicitly trying to master the formalism. The $z$ is indeed complex: it's the same $z$ that appears in Abramowitz & Stegun.
  $endgroup$
  – thb
  8 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I have edited my question to clarify.
  $endgroup$
  – thb
  8 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  +1 for minimizing notation. If necessary the OP can clarify that $0 notin mathbb{N}$.
  $endgroup$
  – Ethan Bolker
  6 hours ago
  

  
  
  
  

add a comment
 | 

1

$begingroup$

I don't like any of these. Too much notation makes questions harder to read, and none of these clarify what $z$ is allowed to be. If $z$ (notice! this is a total guess!) is supposed to be a complex number, I would say, "let $z in mathbb{C}$ be a complex number that is not a non-positive integer."

---

Edit: I've just seen that $z$ is supposed to be an integer. In this case we should just write $z in mathbb{N}$. Most authors define the natural numbers $mathbb{N}$ to be the set of positive integers.

share|cite|improve this answer

edited 8 hours ago

answered 8 hours ago

Rylee LymanRylee Lyman

2,24433 silver badges2020 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, that is how I usually write. Good advice, but today I am explicitly trying to master the formalism. The $z$ is indeed complex: it's the same $z$ that appears in Abramowitz & Stegun.
  $endgroup$
  – thb
  8 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I have edited my question to clarify.
  $endgroup$
  – thb
  8 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  +1 for minimizing notation. If necessary the OP can clarify that $0 notin mathbb{N}$.
  $endgroup$
  – Ethan Bolker
  6 hours ago
  

  
  
  
  

add a comment
 | 

$begingroup$

I don't like any of these. Too much notation makes questions harder to read, and none of these clarify what $z$ is allowed to be. If $z$ (notice! this is a total guess!) is supposed to be a complex number, I would say, "let $z in mathbb{C}$ be a complex number that is not a non-positive integer."

---

Edit: I've just seen that $z$ is supposed to be an integer. In this case we should just write $z in mathbb{N}$. Most authors define the natural numbers $mathbb{N}$ to be the set of positive integers.

share|cite|improve this answer

edited 8 hours ago

answered 8 hours ago

Rylee LymanRylee Lyman

2,24433 silver badges2020 bronze badges

$endgroup$

share|cite|improve this answer

edited 8 hours ago

answered 8 hours ago

Rylee LymanRylee Lyman

2,24433 silver badges2020 bronze badges

answered 8 hours ago

Rylee LymanRylee Lyman

2,24433 silver badges2020 bronze badges

answered 8 hours ago

Rylee LymanRylee Lyman

2,24433 silver badges2020 bronze badges