What is the dot in “1.2.4."












8












$begingroup$


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











$endgroup$








  • 10




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








  • 2




    $begingroup$
    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
    6 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
    6 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
    6 hours ago






  • 4




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
















8












$begingroup$


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











$endgroup$








  • 10




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








  • 2




    $begingroup$
    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
    6 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
    6 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
    6 hours ago






  • 4




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














8












8








8





$begingroup$


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 5 hours ago









anomaly

17.7k42666




17.7k42666










asked 6 hours ago









TuffyTuffy

1675




1675








  • 10




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








  • 2




    $begingroup$
    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
    6 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
    6 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
    6 hours ago






  • 4




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














  • 10




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








  • 2




    $begingroup$
    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
    6 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
    6 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
    6 hours ago






  • 4




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








10




10




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






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






2




2




$begingroup$
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
6 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
6 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
6 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
6 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
6 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
6 hours ago




4




4




$begingroup$
In my (almost entirely English-language) experience the lowered dot for multiplication is used in British sources. Acheson is British.
$endgroup$
– Michael Lugo
5 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
5 hours ago










3 Answers
3






active

oldest

votes


















11












$begingroup$

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
    5 hours ago






  • 8




    $begingroup$
    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
    2 hours ago








  • 4




    $begingroup$
    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
    2 hours ago






  • 1




    $begingroup$
    @mrtaurho, ok, good, that does alleviate my initial shock. :)
    $endgroup$
    – ilkkachu
    2 hours ago






  • 1




    $begingroup$
    @Monty Harder: It is completely nuts for "5.3" to be the same as 5×3. 5.3 is 5 + 3/10 --- Given that Acheson's book appears to take a heavily historical approach (based on what little I can see via google sample previews), it seems pretty obvious to me that he's doing this so as to be using the notation originally used in the 1700s and 1800s. For example, see p. 109 here and p. 49 here.
    $endgroup$
    – Dave L. Renfro
    1 hour ago



















4












$begingroup$

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






share|cite|improve this answer









$endgroup$





















    -1












    $begingroup$

    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
      5 hours ago










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










    • $begingroup$
      @J.W.Tanner I know, I have used that in my comment.
      $endgroup$
      – Wojowu
      5 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
      3 hours ago






    • 2




      $begingroup$
      @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
      3 hours ago











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    3 Answers
    3






    active

    oldest

    votes








    3 Answers
    3






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    11












    $begingroup$

    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
      5 hours ago






    • 8




      $begingroup$
      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
      2 hours ago








    • 4




      $begingroup$
      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
      2 hours ago






    • 1




      $begingroup$
      @mrtaurho, ok, good, that does alleviate my initial shock. :)
      $endgroup$
      – ilkkachu
      2 hours ago






    • 1




      $begingroup$
      @Monty Harder: It is completely nuts for "5.3" to be the same as 5×3. 5.3 is 5 + 3/10 --- Given that Acheson's book appears to take a heavily historical approach (based on what little I can see via google sample previews), it seems pretty obvious to me that he's doing this so as to be using the notation originally used in the 1700s and 1800s. For example, see p. 109 here and p. 49 here.
      $endgroup$
      – Dave L. Renfro
      1 hour ago
















    11












    $begingroup$

    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
      5 hours ago






    • 8




      $begingroup$
      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
      2 hours ago








    • 4




      $begingroup$
      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
      2 hours ago






    • 1




      $begingroup$
      @mrtaurho, ok, good, that does alleviate my initial shock. :)
      $endgroup$
      – ilkkachu
      2 hours ago






    • 1




      $begingroup$
      @Monty Harder: It is completely nuts for "5.3" to be the same as 5×3. 5.3 is 5 + 3/10 --- Given that Acheson's book appears to take a heavily historical approach (based on what little I can see via google sample previews), it seems pretty obvious to me that he's doing this so as to be using the notation originally used in the 1700s and 1800s. For example, see p. 109 here and p. 49 here.
      $endgroup$
      – Dave L. Renfro
      1 hour ago














    11












    11








    11





    $begingroup$

    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 2 hours ago

























    answered 6 hours ago









    mrtaurhomrtaurho

    5,89051641




    5,89051641








    • 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
      5 hours ago






    • 8




      $begingroup$
      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
      2 hours ago








    • 4




      $begingroup$
      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
      2 hours ago






    • 1




      $begingroup$
      @mrtaurho, ok, good, that does alleviate my initial shock. :)
      $endgroup$
      – ilkkachu
      2 hours ago






    • 1




      $begingroup$
      @Monty Harder: It is completely nuts for "5.3" to be the same as 5×3. 5.3 is 5 + 3/10 --- Given that Acheson's book appears to take a heavily historical approach (based on what little I can see via google sample previews), it seems pretty obvious to me that he's doing this so as to be using the notation originally used in the 1700s and 1800s. For example, see p. 109 here and p. 49 here.
      $endgroup$
      – Dave L. Renfro
      1 hour 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
      5 hours ago






    • 8




      $begingroup$
      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
      2 hours ago








    • 4




      $begingroup$
      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
      2 hours ago






    • 1




      $begingroup$
      @mrtaurho, ok, good, that does alleviate my initial shock. :)
      $endgroup$
      – ilkkachu
      2 hours ago






    • 1




      $begingroup$
      @Monty Harder: It is completely nuts for "5.3" to be the same as 5×3. 5.3 is 5 + 3/10 --- Given that Acheson's book appears to take a heavily historical approach (based on what little I can see via google sample previews), it seems pretty obvious to me that he's doing this so as to be using the notation originally used in the 1700s and 1800s. For example, see p. 109 here and p. 49 here.
      $endgroup$
      – Dave L. Renfro
      1 hour 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
    5 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
    5 hours ago




    8




    8




    $begingroup$
    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
    2 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
    2 hours ago






    4




    4




    $begingroup$
    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
    2 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
    2 hours ago




    1




    1




    $begingroup$
    @mrtaurho, ok, good, that does alleviate my initial shock. :)
    $endgroup$
    – ilkkachu
    2 hours ago




    $begingroup$
    @mrtaurho, ok, good, that does alleviate my initial shock. :)
    $endgroup$
    – ilkkachu
    2 hours ago




    1




    1




    $begingroup$
    @Monty Harder: It is completely nuts for "5.3" to be the same as 5×3. 5.3 is 5 + 3/10 --- Given that Acheson's book appears to take a heavily historical approach (based on what little I can see via google sample previews), it seems pretty obvious to me that he's doing this so as to be using the notation originally used in the 1700s and 1800s. For example, see p. 109 here and p. 49 here.
    $endgroup$
    – Dave L. Renfro
    1 hour ago




    $begingroup$
    @Monty Harder: It is completely nuts for "5.3" to be the same as 5×3. 5.3 is 5 + 3/10 --- Given that Acheson's book appears to take a heavily historical approach (based on what little I can see via google sample previews), it seems pretty obvious to me that he's doing this so as to be using the notation originally used in the 1700s and 1800s. For example, see p. 109 here and p. 49 here.
    $endgroup$
    – Dave L. Renfro
    1 hour 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 6 hours ago









        J. W. TannerJ. W. Tanner

        3,1651320




        3,1651320























            -1












            $begingroup$

            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
              5 hours ago










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










            • $begingroup$
              @J.W.Tanner I know, I have used that in my comment.
              $endgroup$
              – Wojowu
              5 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
              3 hours ago






            • 2




              $begingroup$
              @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
              3 hours ago
















            -1












            $begingroup$

            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
              5 hours ago










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










            • $begingroup$
              @J.W.Tanner I know, I have used that in my comment.
              $endgroup$
              – Wojowu
              5 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
              3 hours ago






            • 2




              $begingroup$
              @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
              3 hours ago














            -1












            -1








            -1





            $begingroup$

            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 6 hours ago









            MATHS MODMATHS MOD

            1609




            1609








            • 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
              5 hours ago










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










            • $begingroup$
              @J.W.Tanner I know, I have used that in my comment.
              $endgroup$
              – Wojowu
              5 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
              3 hours ago






            • 2




              $begingroup$
              @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
              3 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
              5 hours ago










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










            • $begingroup$
              @J.W.Tanner I know, I have used that in my comment.
              $endgroup$
              – Wojowu
              5 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
              3 hours ago






            • 2




              $begingroup$
              @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
              3 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
            5 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
            5 hours ago












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




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












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




            $begingroup$
            @J.W.Tanner I know, I have used that in my comment.
            $endgroup$
            – Wojowu
            5 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
            3 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
            3 hours ago




            2




            2




            $begingroup$
            @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
            3 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
            3 hours ago


















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