Is the division symbol $div$ acceptable based on international standards? [closed]
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The division symbol $div$ is found in almost all calculators; however, I seldom see it in any formal writing. It seems people almost exclusively prefer $frac{a}{b}$, $a/b$ or $ab^{-1}$ to $adiv b$. Is the symbol $div$ considered outdated today? Is it all right to use it in formal writtings (for example, denote $ab^{-1}$ by $adiv b$ when $a$ and $b$ are elements in a field such that $bneq 0$)?
Edit: Since the question was on hold since it is "opinion based", I would like to reask my question in the following way:
Is the usuage of the symbol $div$ in professional mathematical writtings acceptable based on objective international standards, such as ISO 80000-2?
notation arithmetic binary-operations
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closed as primarily opinion-based by Peter, Jyrki Lahtonen, amWhy, Gibbs, T. Bongers Dec 7 '18 at 1:21
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
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show 3 more comments
$begingroup$
The division symbol $div$ is found in almost all calculators; however, I seldom see it in any formal writing. It seems people almost exclusively prefer $frac{a}{b}$, $a/b$ or $ab^{-1}$ to $adiv b$. Is the symbol $div$ considered outdated today? Is it all right to use it in formal writtings (for example, denote $ab^{-1}$ by $adiv b$ when $a$ and $b$ are elements in a field such that $bneq 0$)?
Edit: Since the question was on hold since it is "opinion based", I would like to reask my question in the following way:
Is the usuage of the symbol $div$ in professional mathematical writtings acceptable based on objective international standards, such as ISO 80000-2?
notation arithmetic binary-operations
$endgroup$
closed as primarily opinion-based by Peter, Jyrki Lahtonen, amWhy, Gibbs, T. Bongers Dec 7 '18 at 1:21
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
4
$begingroup$
But $div$ is just $frac{a}{b}$ with the bullets replaced by $a$ and $b$: $$frac{bullet}{bullet}=frac{a}{b}$$.
$endgroup$
– Dietrich Burde
Dec 6 '18 at 13:41
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I feel its just because the $div$ symbol is inconvenient
$endgroup$
– glowstonetrees
Dec 6 '18 at 13:42
3
$begingroup$
Even if it's never used beyond a certain level, I can't see primary schools giving up on it.
$endgroup$
– J.G.
Dec 6 '18 at 13:43
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@Jean-ClaudeArbaut, I teach college classes and I do not use $div$ frequently; on the other hand, I also do not shun this notation. Is there any standard suggestion from some authorities, such as ISO 80000 specification?
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– Zuriel
Dec 6 '18 at 13:48
$begingroup$
Thanks @Jean-ClaudeArbaut! In fact, $div$ can still be found even in very advanced scientific calculators. I am also wondering when one studies some algebraic structure, if an operation needs to be defined which is alnalogous to division of real numbers, people ever thought about using $div$.
$endgroup$
– Zuriel
Dec 6 '18 at 14:00
|
show 3 more comments
$begingroup$
The division symbol $div$ is found in almost all calculators; however, I seldom see it in any formal writing. It seems people almost exclusively prefer $frac{a}{b}$, $a/b$ or $ab^{-1}$ to $adiv b$. Is the symbol $div$ considered outdated today? Is it all right to use it in formal writtings (for example, denote $ab^{-1}$ by $adiv b$ when $a$ and $b$ are elements in a field such that $bneq 0$)?
Edit: Since the question was on hold since it is "opinion based", I would like to reask my question in the following way:
Is the usuage of the symbol $div$ in professional mathematical writtings acceptable based on objective international standards, such as ISO 80000-2?
notation arithmetic binary-operations
$endgroup$
The division symbol $div$ is found in almost all calculators; however, I seldom see it in any formal writing. It seems people almost exclusively prefer $frac{a}{b}$, $a/b$ or $ab^{-1}$ to $adiv b$. Is the symbol $div$ considered outdated today? Is it all right to use it in formal writtings (for example, denote $ab^{-1}$ by $adiv b$ when $a$ and $b$ are elements in a field such that $bneq 0$)?
Edit: Since the question was on hold since it is "opinion based", I would like to reask my question in the following way:
Is the usuage of the symbol $div$ in professional mathematical writtings acceptable based on objective international standards, such as ISO 80000-2?
notation arithmetic binary-operations
notation arithmetic binary-operations
edited Dec 7 '18 at 3:11
Zuriel
asked Dec 6 '18 at 13:40
ZurielZuriel
1,5931028
1,5931028
closed as primarily opinion-based by Peter, Jyrki Lahtonen, amWhy, Gibbs, T. Bongers Dec 7 '18 at 1:21
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as primarily opinion-based by Peter, Jyrki Lahtonen, amWhy, Gibbs, T. Bongers Dec 7 '18 at 1:21
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
4
$begingroup$
But $div$ is just $frac{a}{b}$ with the bullets replaced by $a$ and $b$: $$frac{bullet}{bullet}=frac{a}{b}$$.
$endgroup$
– Dietrich Burde
Dec 6 '18 at 13:41
$begingroup$
I feel its just because the $div$ symbol is inconvenient
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– glowstonetrees
Dec 6 '18 at 13:42
3
$begingroup$
Even if it's never used beyond a certain level, I can't see primary schools giving up on it.
$endgroup$
– J.G.
Dec 6 '18 at 13:43
$begingroup$
@Jean-ClaudeArbaut, I teach college classes and I do not use $div$ frequently; on the other hand, I also do not shun this notation. Is there any standard suggestion from some authorities, such as ISO 80000 specification?
$endgroup$
– Zuriel
Dec 6 '18 at 13:48
$begingroup$
Thanks @Jean-ClaudeArbaut! In fact, $div$ can still be found even in very advanced scientific calculators. I am also wondering when one studies some algebraic structure, if an operation needs to be defined which is alnalogous to division of real numbers, people ever thought about using $div$.
$endgroup$
– Zuriel
Dec 6 '18 at 14:00
|
show 3 more comments
4
$begingroup$
But $div$ is just $frac{a}{b}$ with the bullets replaced by $a$ and $b$: $$frac{bullet}{bullet}=frac{a}{b}$$.
$endgroup$
– Dietrich Burde
Dec 6 '18 at 13:41
$begingroup$
I feel its just because the $div$ symbol is inconvenient
$endgroup$
– glowstonetrees
Dec 6 '18 at 13:42
3
$begingroup$
Even if it's never used beyond a certain level, I can't see primary schools giving up on it.
$endgroup$
– J.G.
Dec 6 '18 at 13:43
$begingroup$
@Jean-ClaudeArbaut, I teach college classes and I do not use $div$ frequently; on the other hand, I also do not shun this notation. Is there any standard suggestion from some authorities, such as ISO 80000 specification?
$endgroup$
– Zuriel
Dec 6 '18 at 13:48
$begingroup$
Thanks @Jean-ClaudeArbaut! In fact, $div$ can still be found even in very advanced scientific calculators. I am also wondering when one studies some algebraic structure, if an operation needs to be defined which is alnalogous to division of real numbers, people ever thought about using $div$.
$endgroup$
– Zuriel
Dec 6 '18 at 14:00
4
4
$begingroup$
But $div$ is just $frac{a}{b}$ with the bullets replaced by $a$ and $b$: $$frac{bullet}{bullet}=frac{a}{b}$$.
$endgroup$
– Dietrich Burde
Dec 6 '18 at 13:41
$begingroup$
But $div$ is just $frac{a}{b}$ with the bullets replaced by $a$ and $b$: $$frac{bullet}{bullet}=frac{a}{b}$$.
$endgroup$
– Dietrich Burde
Dec 6 '18 at 13:41
$begingroup$
I feel its just because the $div$ symbol is inconvenient
$endgroup$
– glowstonetrees
Dec 6 '18 at 13:42
$begingroup$
I feel its just because the $div$ symbol is inconvenient
$endgroup$
– glowstonetrees
Dec 6 '18 at 13:42
3
3
$begingroup$
Even if it's never used beyond a certain level, I can't see primary schools giving up on it.
$endgroup$
– J.G.
Dec 6 '18 at 13:43
$begingroup$
Even if it's never used beyond a certain level, I can't see primary schools giving up on it.
$endgroup$
– J.G.
Dec 6 '18 at 13:43
$begingroup$
@Jean-ClaudeArbaut, I teach college classes and I do not use $div$ frequently; on the other hand, I also do not shun this notation. Is there any standard suggestion from some authorities, such as ISO 80000 specification?
$endgroup$
– Zuriel
Dec 6 '18 at 13:48
$begingroup$
@Jean-ClaudeArbaut, I teach college classes and I do not use $div$ frequently; on the other hand, I also do not shun this notation. Is there any standard suggestion from some authorities, such as ISO 80000 specification?
$endgroup$
– Zuriel
Dec 6 '18 at 13:48
$begingroup$
Thanks @Jean-ClaudeArbaut! In fact, $div$ can still be found even in very advanced scientific calculators. I am also wondering when one studies some algebraic structure, if an operation needs to be defined which is alnalogous to division of real numbers, people ever thought about using $div$.
$endgroup$
– Zuriel
Dec 6 '18 at 14:00
$begingroup$
Thanks @Jean-ClaudeArbaut! In fact, $div$ can still be found even in very advanced scientific calculators. I am also wondering when one studies some algebraic structure, if an operation needs to be defined which is alnalogous to division of real numbers, people ever thought about using $div$.
$endgroup$
– Zuriel
Dec 6 '18 at 14:00
|
show 3 more comments
2 Answers
2
active
oldest
votes
$begingroup$
The $div$ symbol is outdated and should be avoided.
Quoting from Florian Cajori's book A History of Mathematical Notations.
(Volume I, Chapter III, Part B, Paragraph $243$ A critical Estimate of $:$ and $div$ as Symbols)
In 1923 the National Committee on Mathematical Requirements voiced the following opinion:
"Since neither $div$ nor $:$, as signs of division plays any part in business life, it seems proper to consider only the needs of algebra, and to make more use of the fractional form and (where meaning is clear) of the symbol $/$, and to drop the symbol $div$ in writing algebraic expressions."
$endgroup$
2
$begingroup$
Thank you! The opinion you quoted is 95 years old; is this opinion outdated? :-)
$endgroup$
– Zuriel
Dec 6 '18 at 14:45
$begingroup$
@Zuriel The opinion would be outdated if the majority of current mathematicians thinks it is outdated. I haven't met a mathematician who uses $div$ even once in a while within the past ten years, so let's that speak for itself. This notation can only be seen in low level math, and sometimes on youtube.
$endgroup$
– user614671
Dec 6 '18 at 19:58
$begingroup$
Thanks! So the conclusion is, $div$ is outdated today; furthermore, it was outdated 95 years ago.
$endgroup$
– Zuriel
Dec 6 '18 at 22:46
add a comment |
$begingroup$
Not a definitive answer, but my feeling is that ÷ says "We are doing arithmetic on actual numerical values", so it might be useful in helping non-mathematical readers to follow what's happening, or if you want to distinguish between the division result and the process of getting it.
Example: as a child, it was a revelation to me that $$2÷3=frac23,$$ ie that two thirds are the same as a third of 2, and that making a fraction is the same as dividing two numbers.
It seemed like magic! Suddenly I didn't have to work out that there were $6$ thirds in $2$ and divide that by $3$ to get two of
them—I could just put one number above the other and have the answer.
The same distinction is expressed in the terminology. ÷ has a divisor by which the dividend is divided, while the fraction has a numerator "enumerating" the subunits used and a denominator specifying the "denomination" or kind of subunit.
So they do signify slightly different concepts—it's just that most of the time, the difference isn't relevant and we're better off ignoring it.
Edit: Here's the conceptual difference expressed visually.

$endgroup$
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The $div$ symbol is outdated and should be avoided.
Quoting from Florian Cajori's book A History of Mathematical Notations.
(Volume I, Chapter III, Part B, Paragraph $243$ A critical Estimate of $:$ and $div$ as Symbols)
In 1923 the National Committee on Mathematical Requirements voiced the following opinion:
"Since neither $div$ nor $:$, as signs of division plays any part in business life, it seems proper to consider only the needs of algebra, and to make more use of the fractional form and (where meaning is clear) of the symbol $/$, and to drop the symbol $div$ in writing algebraic expressions."
$endgroup$
2
$begingroup$
Thank you! The opinion you quoted is 95 years old; is this opinion outdated? :-)
$endgroup$
– Zuriel
Dec 6 '18 at 14:45
$begingroup$
@Zuriel The opinion would be outdated if the majority of current mathematicians thinks it is outdated. I haven't met a mathematician who uses $div$ even once in a while within the past ten years, so let's that speak for itself. This notation can only be seen in low level math, and sometimes on youtube.
$endgroup$
– user614671
Dec 6 '18 at 19:58
$begingroup$
Thanks! So the conclusion is, $div$ is outdated today; furthermore, it was outdated 95 years ago.
$endgroup$
– Zuriel
Dec 6 '18 at 22:46
add a comment |
$begingroup$
The $div$ symbol is outdated and should be avoided.
Quoting from Florian Cajori's book A History of Mathematical Notations.
(Volume I, Chapter III, Part B, Paragraph $243$ A critical Estimate of $:$ and $div$ as Symbols)
In 1923 the National Committee on Mathematical Requirements voiced the following opinion:
"Since neither $div$ nor $:$, as signs of division plays any part in business life, it seems proper to consider only the needs of algebra, and to make more use of the fractional form and (where meaning is clear) of the symbol $/$, and to drop the symbol $div$ in writing algebraic expressions."
$endgroup$
2
$begingroup$
Thank you! The opinion you quoted is 95 years old; is this opinion outdated? :-)
$endgroup$
– Zuriel
Dec 6 '18 at 14:45
$begingroup$
@Zuriel The opinion would be outdated if the majority of current mathematicians thinks it is outdated. I haven't met a mathematician who uses $div$ even once in a while within the past ten years, so let's that speak for itself. This notation can only be seen in low level math, and sometimes on youtube.
$endgroup$
– user614671
Dec 6 '18 at 19:58
$begingroup$
Thanks! So the conclusion is, $div$ is outdated today; furthermore, it was outdated 95 years ago.
$endgroup$
– Zuriel
Dec 6 '18 at 22:46
add a comment |
$begingroup$
The $div$ symbol is outdated and should be avoided.
Quoting from Florian Cajori's book A History of Mathematical Notations.
(Volume I, Chapter III, Part B, Paragraph $243$ A critical Estimate of $:$ and $div$ as Symbols)
In 1923 the National Committee on Mathematical Requirements voiced the following opinion:
"Since neither $div$ nor $:$, as signs of division plays any part in business life, it seems proper to consider only the needs of algebra, and to make more use of the fractional form and (where meaning is clear) of the symbol $/$, and to drop the symbol $div$ in writing algebraic expressions."
$endgroup$
The $div$ symbol is outdated and should be avoided.
Quoting from Florian Cajori's book A History of Mathematical Notations.
(Volume I, Chapter III, Part B, Paragraph $243$ A critical Estimate of $:$ and $div$ as Symbols)
In 1923 the National Committee on Mathematical Requirements voiced the following opinion:
"Since neither $div$ nor $:$, as signs of division plays any part in business life, it seems proper to consider only the needs of algebra, and to make more use of the fractional form and (where meaning is clear) of the symbol $/$, and to drop the symbol $div$ in writing algebraic expressions."
answered Dec 6 '18 at 14:41
achille huiachille hui
95.6k5131258
95.6k5131258
2
$begingroup$
Thank you! The opinion you quoted is 95 years old; is this opinion outdated? :-)
$endgroup$
– Zuriel
Dec 6 '18 at 14:45
$begingroup$
@Zuriel The opinion would be outdated if the majority of current mathematicians thinks it is outdated. I haven't met a mathematician who uses $div$ even once in a while within the past ten years, so let's that speak for itself. This notation can only be seen in low level math, and sometimes on youtube.
$endgroup$
– user614671
Dec 6 '18 at 19:58
$begingroup$
Thanks! So the conclusion is, $div$ is outdated today; furthermore, it was outdated 95 years ago.
$endgroup$
– Zuriel
Dec 6 '18 at 22:46
add a comment |
2
$begingroup$
Thank you! The opinion you quoted is 95 years old; is this opinion outdated? :-)
$endgroup$
– Zuriel
Dec 6 '18 at 14:45
$begingroup$
@Zuriel The opinion would be outdated if the majority of current mathematicians thinks it is outdated. I haven't met a mathematician who uses $div$ even once in a while within the past ten years, so let's that speak for itself. This notation can only be seen in low level math, and sometimes on youtube.
$endgroup$
– user614671
Dec 6 '18 at 19:58
$begingroup$
Thanks! So the conclusion is, $div$ is outdated today; furthermore, it was outdated 95 years ago.
$endgroup$
– Zuriel
Dec 6 '18 at 22:46
2
2
$begingroup$
Thank you! The opinion you quoted is 95 years old; is this opinion outdated? :-)
$endgroup$
– Zuriel
Dec 6 '18 at 14:45
$begingroup$
Thank you! The opinion you quoted is 95 years old; is this opinion outdated? :-)
$endgroup$
– Zuriel
Dec 6 '18 at 14:45
$begingroup$
@Zuriel The opinion would be outdated if the majority of current mathematicians thinks it is outdated. I haven't met a mathematician who uses $div$ even once in a while within the past ten years, so let's that speak for itself. This notation can only be seen in low level math, and sometimes on youtube.
$endgroup$
– user614671
Dec 6 '18 at 19:58
$begingroup$
@Zuriel The opinion would be outdated if the majority of current mathematicians thinks it is outdated. I haven't met a mathematician who uses $div$ even once in a while within the past ten years, so let's that speak for itself. This notation can only be seen in low level math, and sometimes on youtube.
$endgroup$
– user614671
Dec 6 '18 at 19:58
$begingroup$
Thanks! So the conclusion is, $div$ is outdated today; furthermore, it was outdated 95 years ago.
$endgroup$
– Zuriel
Dec 6 '18 at 22:46
$begingroup$
Thanks! So the conclusion is, $div$ is outdated today; furthermore, it was outdated 95 years ago.
$endgroup$
– Zuriel
Dec 6 '18 at 22:46
add a comment |
$begingroup$
Not a definitive answer, but my feeling is that ÷ says "We are doing arithmetic on actual numerical values", so it might be useful in helping non-mathematical readers to follow what's happening, or if you want to distinguish between the division result and the process of getting it.
Example: as a child, it was a revelation to me that $$2÷3=frac23,$$ ie that two thirds are the same as a third of 2, and that making a fraction is the same as dividing two numbers.
It seemed like magic! Suddenly I didn't have to work out that there were $6$ thirds in $2$ and divide that by $3$ to get two of
them—I could just put one number above the other and have the answer.
The same distinction is expressed in the terminology. ÷ has a divisor by which the dividend is divided, while the fraction has a numerator "enumerating" the subunits used and a denominator specifying the "denomination" or kind of subunit.
So they do signify slightly different concepts—it's just that most of the time, the difference isn't relevant and we're better off ignoring it.
Edit: Here's the conceptual difference expressed visually.

$endgroup$
add a comment |
$begingroup$
Not a definitive answer, but my feeling is that ÷ says "We are doing arithmetic on actual numerical values", so it might be useful in helping non-mathematical readers to follow what's happening, or if you want to distinguish between the division result and the process of getting it.
Example: as a child, it was a revelation to me that $$2÷3=frac23,$$ ie that two thirds are the same as a third of 2, and that making a fraction is the same as dividing two numbers.
It seemed like magic! Suddenly I didn't have to work out that there were $6$ thirds in $2$ and divide that by $3$ to get two of
them—I could just put one number above the other and have the answer.
The same distinction is expressed in the terminology. ÷ has a divisor by which the dividend is divided, while the fraction has a numerator "enumerating" the subunits used and a denominator specifying the "denomination" or kind of subunit.
So they do signify slightly different concepts—it's just that most of the time, the difference isn't relevant and we're better off ignoring it.
Edit: Here's the conceptual difference expressed visually.

$endgroup$
add a comment |
$begingroup$
Not a definitive answer, but my feeling is that ÷ says "We are doing arithmetic on actual numerical values", so it might be useful in helping non-mathematical readers to follow what's happening, or if you want to distinguish between the division result and the process of getting it.
Example: as a child, it was a revelation to me that $$2÷3=frac23,$$ ie that two thirds are the same as a third of 2, and that making a fraction is the same as dividing two numbers.
It seemed like magic! Suddenly I didn't have to work out that there were $6$ thirds in $2$ and divide that by $3$ to get two of
them—I could just put one number above the other and have the answer.
The same distinction is expressed in the terminology. ÷ has a divisor by which the dividend is divided, while the fraction has a numerator "enumerating" the subunits used and a denominator specifying the "denomination" or kind of subunit.
So they do signify slightly different concepts—it's just that most of the time, the difference isn't relevant and we're better off ignoring it.
Edit: Here's the conceptual difference expressed visually.

$endgroup$
Not a definitive answer, but my feeling is that ÷ says "We are doing arithmetic on actual numerical values", so it might be useful in helping non-mathematical readers to follow what's happening, or if you want to distinguish between the division result and the process of getting it.
Example: as a child, it was a revelation to me that $$2÷3=frac23,$$ ie that two thirds are the same as a third of 2, and that making a fraction is the same as dividing two numbers.
It seemed like magic! Suddenly I didn't have to work out that there were $6$ thirds in $2$ and divide that by $3$ to get two of
them—I could just put one number above the other and have the answer.
The same distinction is expressed in the terminology. ÷ has a divisor by which the dividend is divided, while the fraction has a numerator "enumerating" the subunits used and a denominator specifying the "denomination" or kind of subunit.
So they do signify slightly different concepts—it's just that most of the time, the difference isn't relevant and we're better off ignoring it.
Edit: Here's the conceptual difference expressed visually.

edited Dec 7 '18 at 1:45
answered Dec 6 '18 at 16:52
timtfjtimtfj
1,318318
1,318318
add a comment |
add a comment |
4
$begingroup$
But $div$ is just $frac{a}{b}$ with the bullets replaced by $a$ and $b$: $$frac{bullet}{bullet}=frac{a}{b}$$.
$endgroup$
– Dietrich Burde
Dec 6 '18 at 13:41
$begingroup$
I feel its just because the $div$ symbol is inconvenient
$endgroup$
– glowstonetrees
Dec 6 '18 at 13:42
3
$begingroup$
Even if it's never used beyond a certain level, I can't see primary schools giving up on it.
$endgroup$
– J.G.
Dec 6 '18 at 13:43
$begingroup$
@Jean-ClaudeArbaut, I teach college classes and I do not use $div$ frequently; on the other hand, I also do not shun this notation. Is there any standard suggestion from some authorities, such as ISO 80000 specification?
$endgroup$
– Zuriel
Dec 6 '18 at 13:48
$begingroup$
Thanks @Jean-ClaudeArbaut! In fact, $div$ can still be found even in very advanced scientific calculators. I am also wondering when one studies some algebraic structure, if an operation needs to be defined which is alnalogous to division of real numbers, people ever thought about using $div$.
$endgroup$
– Zuriel
Dec 6 '18 at 14:00