Home page for accesible maths Math 101 Chapter 2: Functions of a real variable 2.28 Standard limits of functions 2.30 Composite function

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2.29 Nonsensical limits

It is dangerous to use $\infty$ in calculations as if it were a number. The following do not make sense:

\infty^{0},\quad\infty-\infty,\quad 0/0,\quad 0^{0},\quad\infty/\infty,\quad% \infty/0,\quad 1/0.

The MATH113 Series and Functions course contains a fuller account of the properties of limits, including the rules for manipulating limits. The above formulæ are still nonsense since they do not satisfy the rules and are ambiguous.