TITLE: What is the dot in "$1.2.4$"?
QUESTION [10 upvotes]: 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 ‘$\cdot$' (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, that $y$ 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
  $\frac{dy}{dt}=\frac{dy}{dx}\cdot \frac{dx}{dt}$ 

What is the dot doing?  I looked at the suggested previous questions about the dot without success.  Does it mean $\&$ (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 

$$e^x=1+x+\frac{x^2}{1.2}+\frac{x^3}{1.2.3}+...$$

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

REPLY [16 votes]: It is a quite common notation, if used, for multiplication, i.e.

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

In your case
$$dy/dx.dx/dt=\frac{dy}{dx}\times\frac{dx}{dt}$$
and
$$e^x=1+x+\frac{x^2}{1.2}+\frac{x^3}{1.2.3}+\cdots=1+x+\frac{x^2}{1\times2}+\frac{x^3}{1\times2\times3}+\cdots$$

REPLY [5 votes]: Sometimes a dot is used for multiplication. 
 Cf. this Wikipedia article.