There are many common psychological phenomena that I find interesting, from a semi-academic perspective. One of them is the sheer difficulty that some people seem to have in accepting the notion that 0.9 recurring (ie. the decimal representation of a number with "0." followed by an infinite string of 9's) is exactly equal to 1. Both decimal expansions represent the exact same number. Some people will go to incredible lengths to try to argue why they are not equal, up to trying to invent new mathematics, and new kinds of numbers, just to forcefully try to make them unequal. (With very little success, of course, because invariably these are people with very little experience and understanding of mathematics, especially math related to the set of real numbers, and their decimal representations.) There are a few quite simple counter-arguments to their assertion that the two decimal representations are not the same number. For example, if 0.9... is not equal to 1, then by ...