We want to construct our definition of number in terms that are consistent with synthetic dimensionality and the constraint on the term "real" by requiring "actuality"
- N Natural number
- Z Integer
- Q Rational
- R Real
Let's look at "natural number" -- which is illustrated in Wikipedia by apples.
Apples are good objects to illustrate this argument, because we could also illustrate numbers with oranges, or some other kind of fruit.
We want to look into this -- following Tobias Dantzig -- and probably a few others, including Queen and Servant of Science
Let's look into the thesis that perhaps "no number is real that is not actual"
Actual numbers are numbers that can measure and describe "actual things" [Is this an adequate definition? Tobias Dantzig says that working with imaginary numbers "produce concrete results" (intro, p.ix)]
Under this view, there are no actual "negative numbers". Negative numbers are computational artefacts.
The actual numbers are "natural numbers" and "integers" and fractions
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