Are they messed up though? There are many variants of integration. There's as many variants of a derivative. There are also many kinds of measure. They all h

Are they messed up though? There are many variants of integration. There's as many variants of a derivative. There are also many kinds of measure. They all have limitations. Usually, the major limitation is handling sparse fields, because most integrals and derivatives do not hail from discrete mathematics. Cantor's devil staircase is exactly one of those things that bridge discrete mathematics, (mostly discrete) number theory and (mostly continuous) analysis.