>>12055823Consider the zeta function
https://en.m.wikipedia.org/wiki/Riemann_zeta_functionIf a functon is bounded in a neighborhood although not defined in a point, then you can describe how the function behave in that point.
How do you define over a singularity? Just study complex analysis. Note that it doesn't implies that the summation 1+2+3+... equals -1/12, it does imply that if you define a generalized function (zeta function) that is the value the function should have in order to behave like a regular function.