Insane numbers (also known as "Numbers of Insanity") are the equivalent of imaginary numbers in Crazy Mathematics. It is important not to confuse insane numbers with irrational numbers such as the square root of two. The way to remember this is with the maxim:
“All insane numbers are irrational numbers, but not all irrational numbers are insane numbers.”
It is a question of serious philosophical debate in Crazy Philosophy of Mathematics circles whether all insane numbers are imaginary or not. Crazy Mathematical Platonists tend to say no, while Crazy Mathematical Non-Platonists tend to say yes.
Properties of insane numbers
Property of Meaninglessness
The most important property of all insane numbers is that they are not recognized by sane mathematicians as being numbers at all. Within sane mathematics, they are not numbers, not letters, not formulas, not theorems, not proofs, not even meaningful expressions.
Property of Incalculability
Almost all insane numbers are incalculable, meaning that they cannot be reached or manipulated using rules or techniques from sane mathematics alone, without involving illegal operations that break the laws of mathematics. These may result in criminal prosecution by the Math Police.