Infinitesimals

A variable $v$ whose limit is zero is called an infinitesimal^3.1. This is written

$$\lim_{v = 0}, \ {\rm or},\ \lim_{v\rightarrow 0},$$

and means that the successive numerical values of $v$ ultimately become and remain less than any positive number however small. Such a variable is said to become indefinitely small or to ultimately vanish.

If $\lim v = l$, then $\lim (v-l) = 0$; that is, the difference between a variable and its limit is an infinitesimal.

Conversely, if the difference between a variable and a constant is an infinitesimal, then the variable approaches the constant as a limit.