Numbers used for modeling impose constraints on the model

Question

In modeling observation we use different numbers. Mostly either positive integers or rationals. Both impose constraints on the model description. Positive integers have exactly one minimal element (and are granular). Integers have no minimal element but are granular etc.

Does there exist numbers in which we have an infinite number of smallest elements? (We could use prime numbers for constructing such a model (such numbers))

Answer 1

I like rational numbers. They're as fine as needed and are computable.