What is the dot in “1.2.4."












9












$begingroup$


I am not a mathematician. I did additional maths O’level back in the stone age but did not pursue maths further (much to my regret).



I am reading David Acheson’s fascinating book ‘The Story of Calculus’ and have just about kept up till I got a use of ‘.’ (dot) that I do not understand. It is in his Chapter 14 ‘an Enigma’ and first occurs here in the context of chain rule:-




Suppose, for instance, thar y is some function of x, and that x itself is a function of some other variable - say t. Then we can, if we wish, consider y as a function of t, and then
dy/dt=dy/dx.dx/dt




What is the dot doing? I looked at the suggested previous questions about the dot without success. Does it mean and (as it does in propositional logic, where P.Q stands for P&Q?



The (or a) mysterious dot corps up again in Chapter 23, about e numbers, on the topic of the Taylor series. Here we find the series




*e^x=1+x+^2/1.2+x^3/1.2.3+...




What is the dot doing here, please? Is it in some way a concatenation? Or what is it?






calculus sequences-and-series limits notation







share|cite|improve this question











$endgroup$








  • 12




    $begingroup$
    Sometimes a dot is used for multiplication
    $endgroup$
    – J. W. Tanner
    9 hours ago








  • 3




    $begingroup$
    Such a use of a dot when used for multiplication however usually occurs centered vertically as such: $acdot b$ typed as a cdot b as opposed to lower like a decimal point as such: $a.b$.
    $endgroup$
    – JMoravitz
    9 hours ago








  • 1




    $begingroup$
    I'm not sure which is more common, but I've certainly seen a number of posts here on MSE that use a period dot to indicate multiplication. I've only ever used a centered dot myself, though.
    $endgroup$
    – Clayton
    9 hours ago






  • 1




    $begingroup$
    If you just type acdot b without initiating mathmode, it doesn't do anything special of course... you need to initiate mathmode first using dollar signs like $acdot b$. See more about how to type with MathJax and $LaTeX$ here by visiting this tutorial
    $endgroup$
    – JMoravitz
    9 hours ago






  • 5




    $begingroup$
    In my (almost entirely English-language) experience the lowered dot for multiplication is used in British sources. Acheson is British.
    $endgroup$
    – Michael Lugo
    8 hours ago
















9












$begingroup$


I am not a mathematician. I did additional maths O’level back in the stone age but did not pursue maths further (much to my regret).



I am reading David Acheson’s fascinating book ‘The Story of Calculus’ and have just about kept up till I got a use of ‘.’ (dot) that I do not understand. It is in his Chapter 14 ‘an Enigma’ and first occurs here in the context of chain rule:-




Suppose, for instance, thar y is some function of x, and that x itself is a function of some other variable - say t. Then we can, if we wish, consider y as a function of t, and then
dy/dt=dy/dx.dx/dt




What is the dot doing? I looked at the suggested previous questions about the dot without success. Does it mean and (as it does in propositional logic, where P.Q stands for P&Q?



The (or a) mysterious dot corps up again in Chapter 23, about e numbers, on the topic of the Taylor series. Here we find the series




*e^x=1+x+^2/1.2+x^3/1.2.3+...




What is the dot doing here, please? Is it in some way a concatenation? Or what is it?






calculus sequences-and-series limits notation







share|cite|improve this question











$endgroup$








  • 12




    $begingroup$
    Sometimes a dot is used for multiplication
    $endgroup$
    – J. W. Tanner
    9 hours ago








  • 3




    $begingroup$
    Such a use of a dot when used for multiplication however usually occurs centered vertically as such: $acdot b$ typed as a cdot b as opposed to lower like a decimal point as such: $a.b$.
    $endgroup$
    – JMoravitz
    9 hours ago








  • 1




    $begingroup$
    I'm not sure which is more common, but I've certainly seen a number of posts here on MSE that use a period dot to indicate multiplication. I've only ever used a centered dot myself, though.
    $endgroup$
    – Clayton
    9 hours ago






  • 1




    $begingroup$
    If you just type acdot b without initiating mathmode, it doesn't do anything special of course... you need to initiate mathmode first using dollar signs like $acdot b$. See more about how to type with MathJax and $LaTeX$ here by visiting this tutorial
    $endgroup$
    – JMoravitz
    9 hours ago






  • 5




    $begingroup$
    In my (almost entirely English-language) experience the lowered dot for multiplication is used in British sources. Acheson is British.
    $endgroup$
    – Michael Lugo
    8 hours ago














9












9








9


1



$begingroup$


I am not a mathematician. I did additional maths O’level back in the stone age but did not pursue maths further (much to my regret).



I am reading David Acheson’s fascinating book ‘The Story of Calculus’ and have just about kept up till I got a use of ‘.’ (dot) that I do not understand. It is in his Chapter 14 ‘an Enigma’ and first occurs here in the context of chain rule:-




Suppose, for instance, thar y is some function of x, and that x itself is a function of some other variable - say t. Then we can, if we wish, consider y as a function of t, and then
dy/dt=dy/dx.dx/dt




What is the dot doing? I looked at the suggested previous questions about the dot without success. Does it mean and (as it does in propositional logic, where P.Q stands for P&Q?



The (or a) mysterious dot corps up again in Chapter 23, about e numbers, on the topic of the Taylor series. Here we find the series




*e^x=1+x+^2/1.2+x^3/1.2.3+...




What is the dot doing here, please? Is it in some way a concatenation? Or what is it?






calculus sequences-and-series limits notation







share|cite|improve this question











$endgroup$




I am not a mathematician. I did additional maths O’level back in the stone age but did not pursue maths further (much to my regret).



I am reading David Acheson’s fascinating book ‘The Story of Calculus’ and have just about kept up till I got a use of ‘.’ (dot) that I do not understand. It is in his Chapter 14 ‘an Enigma’ and first occurs here in the context of chain rule:-




Suppose, for instance, thar y is some function of x, and that x itself is a function of some other variable - say t. Then we can, if we wish, consider y as a function of t, and then
dy/dt=dy/dx.dx/dt




What is the dot doing? I looked at the suggested previous questions about the dot without success. Does it mean and (as it does in propositional logic, where P.Q stands for P&Q?



The (or a) mysterious dot corps up again in Chapter 23, about e numbers, on the topic of the Taylor series. Here we find the series




*e^x=1+x+^2/1.2+x^3/1.2.3+...




What is the dot doing here, please? Is it in some way a concatenation? Or what is it?






calculus sequences-and-series limits notation




calculus sequences-and-series limits notation






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 9 hours ago









anomaly

17.7k42666




17.7k42666










asked 9 hours ago









TuffyTuffy

1725




1725








  • 12




    $begingroup$
    Sometimes a dot is used for multiplication
    $endgroup$
    – J. W. Tanner
    9 hours ago








  • 3




    $begingroup$
    Such a use of a dot when used for multiplication however usually occurs centered vertically as such: $acdot b$ typed as a cdot b as opposed to lower like a decimal point as such: $a.b$.
    $endgroup$
    – JMoravitz
    9 hours ago








  • 1




    $begingroup$
    I'm not sure which is more common, but I've certainly seen a number of posts here on MSE that use a period dot to indicate multiplication. I've only ever used a centered dot myself, though.
    $endgroup$
    – Clayton
    9 hours ago






  • 1




    $begingroup$
    If you just type acdot b without initiating mathmode, it doesn't do anything special of course... you need to initiate mathmode first using dollar signs like $acdot b$. See more about how to type with MathJax and $LaTeX$ here by visiting this tutorial
    $endgroup$
    – JMoravitz
    9 hours ago






  • 5




    $begingroup$
    In my (almost entirely English-language) experience the lowered dot for multiplication is used in British sources. Acheson is British.
    $endgroup$
    – Michael Lugo
    8 hours ago














  • 12




    $begingroup$
    Sometimes a dot is used for multiplication
    $endgroup$
    – J. W. Tanner
    9 hours ago








  • 3




    $begingroup$
    Such a use of a dot when used for multiplication however usually occurs centered vertically as such: $acdot b$ typed as a cdot b as opposed to lower like a decimal point as such: $a.b$.
    $endgroup$
    – JMoravitz
    9 hours ago








  • 1




    $begingroup$
    I'm not sure which is more common, but I've certainly seen a number of posts here on MSE that use a period dot to indicate multiplication. I've only ever used a centered dot myself, though.
    $endgroup$
    – Clayton
    9 hours ago






  • 1




    $begingroup$
    If you just type acdot b without initiating mathmode, it doesn't do anything special of course... you need to initiate mathmode first using dollar signs like $acdot b$. See more about how to type with MathJax and $LaTeX$ here by visiting this tutorial
    $endgroup$
    – JMoravitz
    9 hours ago






  • 5




    $begingroup$
    In my (almost entirely English-language) experience the lowered dot for multiplication is used in British sources. Acheson is British.
    $endgroup$
    – Michael Lugo
    8 hours ago








12




12




$begingroup$
Sometimes a dot is used for multiplication
$endgroup$
– J. W. Tanner
9 hours ago






$begingroup$
Sometimes a dot is used for multiplication
$endgroup$
– J. W. Tanner
9 hours ago






3




3




$begingroup$
Such a use of a dot when used for multiplication however usually occurs centered vertically as such: $acdot b$ typed as a cdot b as opposed to lower like a decimal point as such: $a.b$.
$endgroup$
– JMoravitz
9 hours ago






$begingroup$
Such a use of a dot when used for multiplication however usually occurs centered vertically as such: $acdot b$ typed as a cdot b as opposed to lower like a decimal point as such: $a.b$.
$endgroup$
– JMoravitz
9 hours ago






1




1




$begingroup$
I'm not sure which is more common, but I've certainly seen a number of posts here on MSE that use a period dot to indicate multiplication. I've only ever used a centered dot myself, though.
$endgroup$
– Clayton
9 hours ago




$begingroup$
I'm not sure which is more common, but I've certainly seen a number of posts here on MSE that use a period dot to indicate multiplication. I've only ever used a centered dot myself, though.
$endgroup$
– Clayton
9 hours ago




1




1




$begingroup$
If you just type acdot b without initiating mathmode, it doesn't do anything special of course... you need to initiate mathmode first using dollar signs like $acdot b$. See more about how to type with MathJax and $LaTeX$ here by visiting this tutorial
$endgroup$
– JMoravitz
9 hours ago




$begingroup$
If you just type acdot b without initiating mathmode, it doesn't do anything special of course... you need to initiate mathmode first using dollar signs like $acdot b$. See more about how to type with MathJax and $LaTeX$ here by visiting this tutorial
$endgroup$
– JMoravitz
9 hours ago




5




5




$begingroup$
In my (almost entirely English-language) experience the lowered dot for multiplication is used in British sources. Acheson is British.
$endgroup$
– Michael Lugo
8 hours ago




$begingroup$
In my (almost entirely English-language) experience the lowered dot for multiplication is used in British sources. Acheson is British.
$endgroup$
– Michael Lugo
8 hours ago










3 Answers
3






active

oldest

votes


















12












$begingroup$

It is a quite common notation, if used, for multiplication, i.e.




$$5.3=5cdot3=5times3=15$$




In your case



$$dy/dx.dx/dt=frac{dy}{dy}timesfrac{dx}{dt}$$
and
$$e^x=1+x+frac{x^2}{1.2}+frac{x^3}{1.2.3}+cdots=1+x+frac{x^2}{1times2}+frac{x^3}{1times2times3}+cdots$$






share|cite|improve this answer











$endgroup$









  • 1




    $begingroup$
    I think that’s it, thank you. But does that mean in the second example that “x^3/1.2.3” means “x^3/1x2x3”?
    $endgroup$
    – Tuffy
    9 hours ago






  • 13




    $begingroup$
    Is the low dot actually really "commonly" used for multiplication? Where? I can understand $x.y$, and $5 cdot 3$ is obviously multiplication, but wouldn't $5.3$ get confused with the number $5 + 3/10$ really fast?!
    $endgroup$
    – ilkkachu
    5 hours ago








  • 5




    $begingroup$
    It is completely nuts for "5.3" to be the same as 5×3. 5.3 is 5 + 3/10, and you can't overload the same symbol to mean something totally different. (letting dx.dx be dx × dx is tolerable, because dx.dx does not already mean dx + dx/10).
    $endgroup$
    – Monty Harder
    5 hours ago






  • 2




    $begingroup$
    @ilkkachu Especially in the field of algebra, specifically in Linear Algebra and Abstract Algeba, I have encountered this notation quite often denoting multiplication, e.g. an inner product, in various ways. For myself, as German native speaker, I am used to $5color{red}{,}3$ as equivalent to $5+frac3{10}$ from where it cannot be mistaken with $5.3$. I have to admit that I have seen this notation rarely in connection with actual multplication of numbers.
    $endgroup$
    – mrtaurho
    5 hours ago






  • 1




    $begingroup$
    @ilkkachu In fact, I have solely encountered this notation in connection with either inner products of vectors spaces or as product of two groups. Take a look a this video:matterhorn.dce.harvard.edu/engage/player/… , right in the begin defining the group $G$ as product of two other groups, namely $G=mathbb R^2color{red}{.}O(2)$.
    $endgroup$
    – mrtaurho
    5 hours ago





















4












$begingroup$

Sometimes a dot is used for multiplication.
Cf. this Wikipedia article.






share|cite|improve this answer









$endgroup$





















    0












    $begingroup$

    As @J.W.Tanner said though we usually write $a$ times $b$ as $$ab$$ or $$a times b$$ the urge of denoting it by $$a cdot b$$ is also common.






    share|cite|improve this answer









    $endgroup$









    • 1




      $begingroup$
      I'm not sure who "we" is in this answer. Among mathematicians, multiplication of numbers is almost universally denoted by $ab$ or $acdot b$. $times$ is used to denote other kinds of products, like the cross product of vectors.
      $endgroup$
      – Wojowu
      8 hours ago










    • $begingroup$
      @Wojowu: note that $times$ is "times" in MathJax
      $endgroup$
      – J. W. Tanner
      8 hours ago










    • $begingroup$
      @J.W.Tanner I know, I have used that in my comment.
      $endgroup$
      – Wojowu
      8 hours ago






    • 1




      $begingroup$
      @Wojowu I think I'd be a little more precise: multiplication of numerical variables is almost always $ab$ or $acdot b$, with $times$ used for other kinds of products. But for multiplying literal numbers, a lot of people will write, e.g., $3times 5$ because $3cdot5$ looks a lot like $3.5$ (and, obviously, $35$ is thirty-five, not fifteen).
      $endgroup$
      – David Richerby
      6 hours ago






    • 3




      $begingroup$
      @DavidRicherby I admit I have meant numerical variables there; of course concatenation would be a terrible choice of a notation. I would still think that, for concrete numbers, $3cdot 5$ would be more common than $3times 5$ (though I admit I'm having hard time finding evidence for that - most math papers nowadays don't multiply numbers!)
      $endgroup$
      – Wojowu
      6 hours ago











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    3 Answers
    3






    active

    oldest

    votes








    3 Answers
    3






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    12












    $begingroup$

    It is a quite common notation, if used, for multiplication, i.e.




    $$5.3=5cdot3=5times3=15$$




    In your case



    $$dy/dx.dx/dt=frac{dy}{dy}timesfrac{dx}{dt}$$
    and
    $$e^x=1+x+frac{x^2}{1.2}+frac{x^3}{1.2.3}+cdots=1+x+frac{x^2}{1times2}+frac{x^3}{1times2times3}+cdots$$






    share|cite|improve this answer











    $endgroup$









    • 1




      $begingroup$
      I think that’s it, thank you. But does that mean in the second example that “x^3/1.2.3” means “x^3/1x2x3”?
      $endgroup$
      – Tuffy
      9 hours ago






    • 13




      $begingroup$
      Is the low dot actually really "commonly" used for multiplication? Where? I can understand $x.y$, and $5 cdot 3$ is obviously multiplication, but wouldn't $5.3$ get confused with the number $5 + 3/10$ really fast?!
      $endgroup$
      – ilkkachu
      5 hours ago








    • 5




      $begingroup$
      It is completely nuts for "5.3" to be the same as 5×3. 5.3 is 5 + 3/10, and you can't overload the same symbol to mean something totally different. (letting dx.dx be dx × dx is tolerable, because dx.dx does not already mean dx + dx/10).
      $endgroup$
      – Monty Harder
      5 hours ago






    • 2




      $begingroup$
      @ilkkachu Especially in the field of algebra, specifically in Linear Algebra and Abstract Algeba, I have encountered this notation quite often denoting multiplication, e.g. an inner product, in various ways. For myself, as German native speaker, I am used to $5color{red}{,}3$ as equivalent to $5+frac3{10}$ from where it cannot be mistaken with $5.3$. I have to admit that I have seen this notation rarely in connection with actual multplication of numbers.
      $endgroup$
      – mrtaurho
      5 hours ago






    • 1




      $begingroup$
      @ilkkachu In fact, I have solely encountered this notation in connection with either inner products of vectors spaces or as product of two groups. Take a look a this video:matterhorn.dce.harvard.edu/engage/player/… , right in the begin defining the group $G$ as product of two other groups, namely $G=mathbb R^2color{red}{.}O(2)$.
      $endgroup$
      – mrtaurho
      5 hours ago


















    12












    $begingroup$

    It is a quite common notation, if used, for multiplication, i.e.




    $$5.3=5cdot3=5times3=15$$




    In your case



    $$dy/dx.dx/dt=frac{dy}{dy}timesfrac{dx}{dt}$$
    and
    $$e^x=1+x+frac{x^2}{1.2}+frac{x^3}{1.2.3}+cdots=1+x+frac{x^2}{1times2}+frac{x^3}{1times2times3}+cdots$$






    share|cite|improve this answer











    $endgroup$









    • 1




      $begingroup$
      I think that’s it, thank you. But does that mean in the second example that “x^3/1.2.3” means “x^3/1x2x3”?
      $endgroup$
      – Tuffy
      9 hours ago






    • 13




      $begingroup$
      Is the low dot actually really "commonly" used for multiplication? Where? I can understand $x.y$, and $5 cdot 3$ is obviously multiplication, but wouldn't $5.3$ get confused with the number $5 + 3/10$ really fast?!
      $endgroup$
      – ilkkachu
      5 hours ago








    • 5




      $begingroup$
      It is completely nuts for "5.3" to be the same as 5×3. 5.3 is 5 + 3/10, and you can't overload the same symbol to mean something totally different. (letting dx.dx be dx × dx is tolerable, because dx.dx does not already mean dx + dx/10).
      $endgroup$
      – Monty Harder
      5 hours ago






    • 2




      $begingroup$
      @ilkkachu Especially in the field of algebra, specifically in Linear Algebra and Abstract Algeba, I have encountered this notation quite often denoting multiplication, e.g. an inner product, in various ways. For myself, as German native speaker, I am used to $5color{red}{,}3$ as equivalent to $5+frac3{10}$ from where it cannot be mistaken with $5.3$. I have to admit that I have seen this notation rarely in connection with actual multplication of numbers.
      $endgroup$
      – mrtaurho
      5 hours ago






    • 1




      $begingroup$
      @ilkkachu In fact, I have solely encountered this notation in connection with either inner products of vectors spaces or as product of two groups. Take a look a this video:matterhorn.dce.harvard.edu/engage/player/… , right in the begin defining the group $G$ as product of two other groups, namely $G=mathbb R^2color{red}{.}O(2)$.
      $endgroup$
      – mrtaurho
      5 hours ago
















    12












    12








    12





    $begingroup$

    It is a quite common notation, if used, for multiplication, i.e.




    $$5.3=5cdot3=5times3=15$$




    In your case



    $$dy/dx.dx/dt=frac{dy}{dy}timesfrac{dx}{dt}$$
    and
    $$e^x=1+x+frac{x^2}{1.2}+frac{x^3}{1.2.3}+cdots=1+x+frac{x^2}{1times2}+frac{x^3}{1times2times3}+cdots$$






    share|cite|improve this answer











    $endgroup$



    It is a quite common notation, if used, for multiplication, i.e.




    $$5.3=5cdot3=5times3=15$$




    In your case



    $$dy/dx.dx/dt=frac{dy}{dy}timesfrac{dx}{dt}$$
    and
    $$e^x=1+x+frac{x^2}{1.2}+frac{x^3}{1.2.3}+cdots=1+x+frac{x^2}{1times2}+frac{x^3}{1times2times3}+cdots$$







    share|cite|improve this answer














    share|cite|improve this answer



    share|cite|improve this answer








    edited 5 hours ago

























    answered 9 hours ago









    mrtaurhomrtaurho

    5,93551641




    5,93551641








    • 1




      $begingroup$
      I think that’s it, thank you. But does that mean in the second example that “x^3/1.2.3” means “x^3/1x2x3”?
      $endgroup$
      – Tuffy
      9 hours ago






    • 13




      $begingroup$
      Is the low dot actually really "commonly" used for multiplication? Where? I can understand $x.y$, and $5 cdot 3$ is obviously multiplication, but wouldn't $5.3$ get confused with the number $5 + 3/10$ really fast?!
      $endgroup$
      – ilkkachu
      5 hours ago








    • 5




      $begingroup$
      It is completely nuts for "5.3" to be the same as 5×3. 5.3 is 5 + 3/10, and you can't overload the same symbol to mean something totally different. (letting dx.dx be dx × dx is tolerable, because dx.dx does not already mean dx + dx/10).
      $endgroup$
      – Monty Harder
      5 hours ago






    • 2




      $begingroup$
      @ilkkachu Especially in the field of algebra, specifically in Linear Algebra and Abstract Algeba, I have encountered this notation quite often denoting multiplication, e.g. an inner product, in various ways. For myself, as German native speaker, I am used to $5color{red}{,}3$ as equivalent to $5+frac3{10}$ from where it cannot be mistaken with $5.3$. I have to admit that I have seen this notation rarely in connection with actual multplication of numbers.
      $endgroup$
      – mrtaurho
      5 hours ago






    • 1




      $begingroup$
      @ilkkachu In fact, I have solely encountered this notation in connection with either inner products of vectors spaces or as product of two groups. Take a look a this video:matterhorn.dce.harvard.edu/engage/player/… , right in the begin defining the group $G$ as product of two other groups, namely $G=mathbb R^2color{red}{.}O(2)$.
      $endgroup$
      – mrtaurho
      5 hours ago
















    • 1




      $begingroup$
      I think that’s it, thank you. But does that mean in the second example that “x^3/1.2.3” means “x^3/1x2x3”?
      $endgroup$
      – Tuffy
      9 hours ago






    • 13




      $begingroup$
      Is the low dot actually really "commonly" used for multiplication? Where? I can understand $x.y$, and $5 cdot 3$ is obviously multiplication, but wouldn't $5.3$ get confused with the number $5 + 3/10$ really fast?!
      $endgroup$
      – ilkkachu
      5 hours ago








    • 5




      $begingroup$
      It is completely nuts for "5.3" to be the same as 5×3. 5.3 is 5 + 3/10, and you can't overload the same symbol to mean something totally different. (letting dx.dx be dx × dx is tolerable, because dx.dx does not already mean dx + dx/10).
      $endgroup$
      – Monty Harder
      5 hours ago






    • 2




      $begingroup$
      @ilkkachu Especially in the field of algebra, specifically in Linear Algebra and Abstract Algeba, I have encountered this notation quite often denoting multiplication, e.g. an inner product, in various ways. For myself, as German native speaker, I am used to $5color{red}{,}3$ as equivalent to $5+frac3{10}$ from where it cannot be mistaken with $5.3$. I have to admit that I have seen this notation rarely in connection with actual multplication of numbers.
      $endgroup$
      – mrtaurho
      5 hours ago






    • 1




      $begingroup$
      @ilkkachu In fact, I have solely encountered this notation in connection with either inner products of vectors spaces or as product of two groups. Take a look a this video:matterhorn.dce.harvard.edu/engage/player/… , right in the begin defining the group $G$ as product of two other groups, namely $G=mathbb R^2color{red}{.}O(2)$.
      $endgroup$
      – mrtaurho
      5 hours ago










    1




    1




    $begingroup$
    I think that’s it, thank you. But does that mean in the second example that “x^3/1.2.3” means “x^3/1x2x3”?
    $endgroup$
    – Tuffy
    9 hours ago




    $begingroup$
    I think that’s it, thank you. But does that mean in the second example that “x^3/1.2.3” means “x^3/1x2x3”?
    $endgroup$
    – Tuffy
    9 hours ago




    13




    13




    $begingroup$
    Is the low dot actually really "commonly" used for multiplication? Where? I can understand $x.y$, and $5 cdot 3$ is obviously multiplication, but wouldn't $5.3$ get confused with the number $5 + 3/10$ really fast?!
    $endgroup$
    – ilkkachu
    5 hours ago






    $begingroup$
    Is the low dot actually really "commonly" used for multiplication? Where? I can understand $x.y$, and $5 cdot 3$ is obviously multiplication, but wouldn't $5.3$ get confused with the number $5 + 3/10$ really fast?!
    $endgroup$
    – ilkkachu
    5 hours ago






    5




    5




    $begingroup$
    It is completely nuts for "5.3" to be the same as 5×3. 5.3 is 5 + 3/10, and you can't overload the same symbol to mean something totally different. (letting dx.dx be dx × dx is tolerable, because dx.dx does not already mean dx + dx/10).
    $endgroup$
    – Monty Harder
    5 hours ago




    $begingroup$
    It is completely nuts for "5.3" to be the same as 5×3. 5.3 is 5 + 3/10, and you can't overload the same symbol to mean something totally different. (letting dx.dx be dx × dx is tolerable, because dx.dx does not already mean dx + dx/10).
    $endgroup$
    – Monty Harder
    5 hours ago




    2




    2




    $begingroup$
    @ilkkachu Especially in the field of algebra, specifically in Linear Algebra and Abstract Algeba, I have encountered this notation quite often denoting multiplication, e.g. an inner product, in various ways. For myself, as German native speaker, I am used to $5color{red}{,}3$ as equivalent to $5+frac3{10}$ from where it cannot be mistaken with $5.3$. I have to admit that I have seen this notation rarely in connection with actual multplication of numbers.
    $endgroup$
    – mrtaurho
    5 hours ago




    $begingroup$
    @ilkkachu Especially in the field of algebra, specifically in Linear Algebra and Abstract Algeba, I have encountered this notation quite often denoting multiplication, e.g. an inner product, in various ways. For myself, as German native speaker, I am used to $5color{red}{,}3$ as equivalent to $5+frac3{10}$ from where it cannot be mistaken with $5.3$. I have to admit that I have seen this notation rarely in connection with actual multplication of numbers.
    $endgroup$
    – mrtaurho
    5 hours ago




    1




    1




    $begingroup$
    @ilkkachu In fact, I have solely encountered this notation in connection with either inner products of vectors spaces or as product of two groups. Take a look a this video:matterhorn.dce.harvard.edu/engage/player/… , right in the begin defining the group $G$ as product of two other groups, namely $G=mathbb R^2color{red}{.}O(2)$.
    $endgroup$
    – mrtaurho
    5 hours ago






    $begingroup$
    @ilkkachu In fact, I have solely encountered this notation in connection with either inner products of vectors spaces or as product of two groups. Take a look a this video:matterhorn.dce.harvard.edu/engage/player/… , right in the begin defining the group $G$ as product of two other groups, namely $G=mathbb R^2color{red}{.}O(2)$.
    $endgroup$
    – mrtaurho
    5 hours ago













    4












    $begingroup$

    Sometimes a dot is used for multiplication.
    Cf. this Wikipedia article.






    share|cite|improve this answer









    $endgroup$


















      4












      $begingroup$

      Sometimes a dot is used for multiplication.
      Cf. this Wikipedia article.






      share|cite|improve this answer









      $endgroup$
















        4












        4








        4





        $begingroup$

        Sometimes a dot is used for multiplication.
        Cf. this Wikipedia article.






        share|cite|improve this answer









        $endgroup$



        Sometimes a dot is used for multiplication.
        Cf. this Wikipedia article.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 9 hours ago









        J. W. TannerJ. W. Tanner

        3,2001320




        3,2001320























            0












            $begingroup$

            As @J.W.Tanner said though we usually write $a$ times $b$ as $$ab$$ or $$a times b$$ the urge of denoting it by $$a cdot b$$ is also common.






            share|cite|improve this answer









            $endgroup$









            • 1




              $begingroup$
              I'm not sure who "we" is in this answer. Among mathematicians, multiplication of numbers is almost universally denoted by $ab$ or $acdot b$. $times$ is used to denote other kinds of products, like the cross product of vectors.
              $endgroup$
              – Wojowu
              8 hours ago










            • $begingroup$
              @Wojowu: note that $times$ is "times" in MathJax
              $endgroup$
              – J. W. Tanner
              8 hours ago










            • $begingroup$
              @J.W.Tanner I know, I have used that in my comment.
              $endgroup$
              – Wojowu
              8 hours ago






            • 1




              $begingroup$
              @Wojowu I think I'd be a little more precise: multiplication of numerical variables is almost always $ab$ or $acdot b$, with $times$ used for other kinds of products. But for multiplying literal numbers, a lot of people will write, e.g., $3times 5$ because $3cdot5$ looks a lot like $3.5$ (and, obviously, $35$ is thirty-five, not fifteen).
              $endgroup$
              – David Richerby
              6 hours ago






            • 3




              $begingroup$
              @DavidRicherby I admit I have meant numerical variables there; of course concatenation would be a terrible choice of a notation. I would still think that, for concrete numbers, $3cdot 5$ would be more common than $3times 5$ (though I admit I'm having hard time finding evidence for that - most math papers nowadays don't multiply numbers!)
              $endgroup$
              – Wojowu
              6 hours ago
















            0












            $begingroup$

            As @J.W.Tanner said though we usually write $a$ times $b$ as $$ab$$ or $$a times b$$ the urge of denoting it by $$a cdot b$$ is also common.






            share|cite|improve this answer









            $endgroup$









            • 1




              $begingroup$
              I'm not sure who "we" is in this answer. Among mathematicians, multiplication of numbers is almost universally denoted by $ab$ or $acdot b$. $times$ is used to denote other kinds of products, like the cross product of vectors.
              $endgroup$
              – Wojowu
              8 hours ago










            • $begingroup$
              @Wojowu: note that $times$ is "times" in MathJax
              $endgroup$
              – J. W. Tanner
              8 hours ago










            • $begingroup$
              @J.W.Tanner I know, I have used that in my comment.
              $endgroup$
              – Wojowu
              8 hours ago






            • 1




              $begingroup$
              @Wojowu I think I'd be a little more precise: multiplication of numerical variables is almost always $ab$ or $acdot b$, with $times$ used for other kinds of products. But for multiplying literal numbers, a lot of people will write, e.g., $3times 5$ because $3cdot5$ looks a lot like $3.5$ (and, obviously, $35$ is thirty-five, not fifteen).
              $endgroup$
              – David Richerby
              6 hours ago






            • 3




              $begingroup$
              @DavidRicherby I admit I have meant numerical variables there; of course concatenation would be a terrible choice of a notation. I would still think that, for concrete numbers, $3cdot 5$ would be more common than $3times 5$ (though I admit I'm having hard time finding evidence for that - most math papers nowadays don't multiply numbers!)
              $endgroup$
              – Wojowu
              6 hours ago














            0












            0








            0





            $begingroup$

            As @J.W.Tanner said though we usually write $a$ times $b$ as $$ab$$ or $$a times b$$ the urge of denoting it by $$a cdot b$$ is also common.






            share|cite|improve this answer









            $endgroup$



            As @J.W.Tanner said though we usually write $a$ times $b$ as $$ab$$ or $$a times b$$ the urge of denoting it by $$a cdot b$$ is also common.







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered 9 hours ago









            MATHS MODMATHS MOD

            1709




            1709








            • 1




              $begingroup$
              I'm not sure who "we" is in this answer. Among mathematicians, multiplication of numbers is almost universally denoted by $ab$ or $acdot b$. $times$ is used to denote other kinds of products, like the cross product of vectors.
              $endgroup$
              – Wojowu
              8 hours ago










            • $begingroup$
              @Wojowu: note that $times$ is "times" in MathJax
              $endgroup$
              – J. W. Tanner
              8 hours ago










            • $begingroup$
              @J.W.Tanner I know, I have used that in my comment.
              $endgroup$
              – Wojowu
              8 hours ago






            • 1




              $begingroup$
              @Wojowu I think I'd be a little more precise: multiplication of numerical variables is almost always $ab$ or $acdot b$, with $times$ used for other kinds of products. But for multiplying literal numbers, a lot of people will write, e.g., $3times 5$ because $3cdot5$ looks a lot like $3.5$ (and, obviously, $35$ is thirty-five, not fifteen).
              $endgroup$
              – David Richerby
              6 hours ago






            • 3




              $begingroup$
              @DavidRicherby I admit I have meant numerical variables there; of course concatenation would be a terrible choice of a notation. I would still think that, for concrete numbers, $3cdot 5$ would be more common than $3times 5$ (though I admit I'm having hard time finding evidence for that - most math papers nowadays don't multiply numbers!)
              $endgroup$
              – Wojowu
              6 hours ago














            • 1




              $begingroup$
              I'm not sure who "we" is in this answer. Among mathematicians, multiplication of numbers is almost universally denoted by $ab$ or $acdot b$. $times$ is used to denote other kinds of products, like the cross product of vectors.
              $endgroup$
              – Wojowu
              8 hours ago










            • $begingroup$
              @Wojowu: note that $times$ is "times" in MathJax
              $endgroup$
              – J. W. Tanner
              8 hours ago










            • $begingroup$
              @J.W.Tanner I know, I have used that in my comment.
              $endgroup$
              – Wojowu
              8 hours ago






            • 1




              $begingroup$
              @Wojowu I think I'd be a little more precise: multiplication of numerical variables is almost always $ab$ or $acdot b$, with $times$ used for other kinds of products. But for multiplying literal numbers, a lot of people will write, e.g., $3times 5$ because $3cdot5$ looks a lot like $3.5$ (and, obviously, $35$ is thirty-five, not fifteen).
              $endgroup$
              – David Richerby
              6 hours ago






            • 3




              $begingroup$
              @DavidRicherby I admit I have meant numerical variables there; of course concatenation would be a terrible choice of a notation. I would still think that, for concrete numbers, $3cdot 5$ would be more common than $3times 5$ (though I admit I'm having hard time finding evidence for that - most math papers nowadays don't multiply numbers!)
              $endgroup$
              – Wojowu
              6 hours ago








            1




            1




            $begingroup$
            I'm not sure who "we" is in this answer. Among mathematicians, multiplication of numbers is almost universally denoted by $ab$ or $acdot b$. $times$ is used to denote other kinds of products, like the cross product of vectors.
            $endgroup$
            – Wojowu
            8 hours ago




            $begingroup$
            I'm not sure who "we" is in this answer. Among mathematicians, multiplication of numbers is almost universally denoted by $ab$ or $acdot b$. $times$ is used to denote other kinds of products, like the cross product of vectors.
            $endgroup$
            – Wojowu
            8 hours ago












            $begingroup$
            @Wojowu: note that $times$ is "times" in MathJax
            $endgroup$
            – J. W. Tanner
            8 hours ago




            $begingroup$
            @Wojowu: note that $times$ is "times" in MathJax
            $endgroup$
            – J. W. Tanner
            8 hours ago












            $begingroup$
            @J.W.Tanner I know, I have used that in my comment.
            $endgroup$
            – Wojowu
            8 hours ago




            $begingroup$
            @J.W.Tanner I know, I have used that in my comment.
            $endgroup$
            – Wojowu
            8 hours ago




            1




            1




            $begingroup$
            @Wojowu I think I'd be a little more precise: multiplication of numerical variables is almost always $ab$ or $acdot b$, with $times$ used for other kinds of products. But for multiplying literal numbers, a lot of people will write, e.g., $3times 5$ because $3cdot5$ looks a lot like $3.5$ (and, obviously, $35$ is thirty-five, not fifteen).
            $endgroup$
            – David Richerby
            6 hours ago




            $begingroup$
            @Wojowu I think I'd be a little more precise: multiplication of numerical variables is almost always $ab$ or $acdot b$, with $times$ used for other kinds of products. But for multiplying literal numbers, a lot of people will write, e.g., $3times 5$ because $3cdot5$ looks a lot like $3.5$ (and, obviously, $35$ is thirty-five, not fifteen).
            $endgroup$
            – David Richerby
            6 hours ago




            3




            3




            $begingroup$
            @DavidRicherby I admit I have meant numerical variables there; of course concatenation would be a terrible choice of a notation. I would still think that, for concrete numbers, $3cdot 5$ would be more common than $3times 5$ (though I admit I'm having hard time finding evidence for that - most math papers nowadays don't multiply numbers!)
            $endgroup$
            – Wojowu
            6 hours ago




            $begingroup$
            @DavidRicherby I admit I have meant numerical variables there; of course concatenation would be a terrible choice of a notation. I would still think that, for concrete numbers, $3cdot 5$ would be more common than $3times 5$ (though I admit I'm having hard time finding evidence for that - most math papers nowadays don't multiply numbers!)
            $endgroup$
            – Wojowu
            6 hours ago


















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