In this blog post https://medium.com/engineering-housing/nan-is-not-equal-to-nan-771321379694 “NaN is not equal to NaN!”, Dron Rathore discusses the IEEE standard of NaN being a value which is not equal to itself. The blog explains some of the definitions and implementations surrounding NaN. It is not an opinionated blog post, it is mainly for the sake of being an educational resource. My particular interest is the actual reason in the first place for why NaN is defined as not being equal to itself. The result of comparison must be a boolean, so the only options for trying to compare NaN to itself are to return true or false, or error and crash. In mathematics, NaN is effectively “undefined” or “indeterminate”, so something like 0/0 is undefined. The truth value of the equation 0/0 = 0/0 is also undefined; the operation of equality is not defined for values that are not defined themselves unless the operation itself is given additional definition to account for that case, which is what must be done for programming languages so that it results in a boolean value. The choice for that value to be false is peculiar and ultimately seems arbitrary, but it is useful for detecting values that are NaN; if (x == x) is false then x is NaN. This blog post does not directly give any feedback on the reason for this implementation of NaN, it merely describes it, but I would like to get some perspective on how the choice is made and how it is more logical to have NaN not equal to itself over an alternative implementation where it is. Comparisons involving NaN may still result in confusing outputs; infinity > NaN is false, for instance, and so is infinity <= NaN, but “not (infinity <= NaN)” is true. For the sake of software testing, NaN adds a lot of strange edge cases where assumptions about equality lead to contradictions. In these cases, or in any case where it is not okay for NaN to exist, it makes the most sense to just have errors instead of trying to deal with this unique behavior.
From the blog cs-wsu – klapointe blog by klapointe2 and used with permission of the author. All other rights reserved by the author.
