The concept of infinity ($\infty$)

If a variable $v$ ultimately becomes and remains greater than any assigned positive number, however large, we say $v$ ``increases without limit'', and write

$$\lim_{v = +\infty},\ {\rm or},\ \lim_{v\rightarrow +\infty}, \ {\rm or}, \ v\rightarrow +\infty.$$

If a variable $v$ ultimately becomes and remains algebraically less than any assigned negative number, we say ``$v$ decreases without limit'', and write

$$\lim_{v = -\infty},\ {\rm or},\ \lim_{v\rightarrow -\infty}, \ {\rm or}, \ v\rightarrow -\infty.$$

If a variable $v$ ultimately becomes and remains in numerical value greater than any assigned positive number, however large, we say $v$, in numerical value, ``increases without limit'', or $v$ becomes infinitely great^3.2, and write

$$\lim_{v = \infty},\ {\rm or},\ \lim_{v\rightarrow \infty}, \ {\rm or}, \ v\rightarrow \infty.$$

Infinity ($\infty$) is not a number; it simply serves to characterize a particular mode of variation of a variable by virtue of which it increases or decreases without limit.