I need clarity on some definitions and mathematical "skepticism". In a recent video by Matt Parker, he says "(...) although the existence of the sign function, which says if a value is positive or negative, upsets some people (...)".
What does he mean by this, and can this "upsetting" be extended to functions like the absolute value or the indicator function of a set? Any suggestions for further reading would be highly appreciated!
Edit: Before this question is closed, I would like to clarify that by no means is this question intended to incentivize discord or negative emotions regarding certain groups of people. I do not wish to offend, nor suggest I am taking part in any ideology regarding the nature of mathematics and its definitions. I am merely curious about what Matt meant, and what is the deeper motivation behind his brief comment, hopefully generating a healthy discussion. Thank you.
According to the most classical definitions, the sign function is a function and does exist.
However, in some alternative contexts such as intuitionistics / constructive mathematics, the sign function does not exist because it is not a continuous function, and in these mathematics theories, only continous functions do exist.
See for example:
(The question might actually be closed as duplicate, as a more general question exists in MSE, cf. above. But some people might not find it if they have only heard about "the sign function does not exist", which is the usual example, and not "only continuous functions do exist".)