What is the dot in "$1.2.4$"?

Question

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?

Answer 1

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 $$e^x=1+x+\frac{x^2}{1.2}+\frac{x^3}{1.2.3}+\cdots=1+x+\frac{x^2}{1\times2}+\frac{x^3}{1\times2\times3}+\cdots$$

Answer 2

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.

Answer 3

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