What nonsense. (Admittedly sarcasm is not a much better response than supercilious dismissal.) Infinity as a mathematical object, not merely some 19th century epsilon-delta definition, crops up all over in mathematics and there are several senses in which the "square root of infinity" makes sense. Just because the

*real number line*doesn't include "infinity" as a number doesn't mean the question has no answer.

The surreal numbers include a host of transfinite numbers, and not just square roots but arbitrary powers are defined on them. (These can be identified as infinite two-player games as well...)

However, it's easy enough to define a multiplicative semigroup (or monoid) that includes infinity, and note that "inf * inf = inf" so inf is its own square root, which is no more contradictory than '1' being its own multiplicative identity. You just have to admit that it's no longer a group.

IEEE 754 floating point arithmetic has a similar property; try squaring numbers with big exponents and you'll quickly get "infinity" as an answer. These "square roots of infinity" are pretty numerous.

## Error

Your reply will be screened

Your IP address will be recorded

You must follow the Privacy Policy and Google Terms of use.