Mathematical continuum structure
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Much of mathematics is based on a mathematical continuum structure. Mathematics has problems with random discontinuities in numbers systems. Mathematical continuum structures are very useful for science. Two or more physical properties are tied to numbers that are then connected to each other. When you know one number it will also know the other number. Equations allow this type of connection. For instance, the equation x = 2y for every number x there is another number that corresponds to it in y in a one to one relationship to it in a mathematical continuum structure. The mathematics that calculus deals with becomes much more difficult where it is not based on a mathematical continuum structure.