This historical issue about the nature of a "number" also caught my eye. (In the PDF: "Before Newton, the word number referred only to the natural numbers...".

This historical issue about the nature of a "number" also caught my eye. (In the PDF: "Before Newton, the word number referred only to the natural numbers...".) Of course, the notion of irrational numbers dates (at least) back to the classical Greeks (the proof-by-contradiction that root-2 is irrational is ancient and elementary, and will be known to some of your intended audience). In the Greek era, there was debate about the status of the irrationals, but sophisticated Greeks were well-acquainted with rational numbers. The statement in the PDF seems to ignore this. Summary: I think this statement of yours is dubious to begin with, and in any event would have to be so qualified and referenced that its value to a novice is nil.