User blog:Vel!/Bad Infinities

\[1/0\]

Why it doesn't work: Zero is not in the domain of the second argument of the division function.

\[-\log 0\]

Why it doesn't work: Zero is not in the domain of any logarithm function.

\[\infty \text{ in the extended real numbers}\]

Why it doesn't work: Googology is the process of searching for increasingly large finite real numbers. This is not a real number.

\[\lim_{x \rightarrow 0} 1/x\]

Why it doesn't work: The limit is undefined.

\[\lim_{x \rightarrow 0^+} 1/x\]

Why it doesn't work: The limit is undefined. If we allow use of the extended real numbers, we have the same problem as before.

\[x \text{ where } x = 10^x\]

Why it doesn't work: No real number satisfies this property (although an infinite family of complex numbers does).

\[\delta(0) \text{ (Dirac delta function)}\]

Why it doesn't work: The Dirac delta function is only rigorously valid inside an integral.