Limits and Continuity on Two-element Numbers

“„One can give good reasons why reality cannot at all be represented by a continuous field. From the quantum phenomena it appears to follow with certainty that a finite system of finite energy can be completely described by a finite set of numbers (quantum numbers). This does not seem to be in accordance with a continuum theory and must lead to an attempt to find a purely algebraic theory for the description of reality. But nobody knows how to obtain the basis of such a theory.””
(Einstein , The meaning of relativity)

The problem with mathematical continuity is similar to the problem with infinity; continuity in reality is very different from the concept defined in mathematics. Just as we do not experience a quantitative infinite that actually exists, we cannot experience continuity in the sense that mathematics defines it, and the two are causally related.

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