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There are the longstanding differences in the continuity of continuum amongmathematicians. Starting from studies on a mathematical model of contact, weconstruct a set that is in contact everywhere by using the original idea ofDedekind's cut and weakening Order axioms to violate Order axiom 1. It isproved that the existence of the set constructed can eliminate the differencesin the continuity.

A solution for the differences in the continuity of continuum among mathematicians