Numbers start with counting. You can build up more kinds of numbers, but tearing down counting into smaller pieces is surprisingly hard. Personally, I think it's good enough to start with any two distinguishable states. You can then keep combining those states in various ways to form the counting numbers. Note that more complex symbols like "1 2 3" are themselves effectively a form of tally, where you are counting the number of angles. You can combine your method with geometry or a clock and call it "measurement" of space and time, respectively.
(Real numbers are my favorite construction because I was enamored with Cantor's diagonal argument when I first learned it. It's quite clever and hints at the magic mathematicians are capable of. Although most mathematicians (algebra peeps) seem to like the classic "root 2 is irrational" proof more.)
Comments
Numbers start with counting. You can build up more kinds of numbers, but tearing down counting into smaller pieces is surprisingly hard. Personally, I think it's good enough to start with any two distinguishable states. You can then keep combining those states in various ways to form the counting numbers. Note that more complex symbols like "1 2 3" are themselves effectively a form of tally, where you are counting the number of angles. You can combine your method with geometry or a clock and call it "measurement" of space and time, respectively.
(Real numbers are my favorite construction because I was enamored with Cantor's diagonal argument when I first learned it. It's quite clever and hints at the magic mathematicians are capable of. Although most mathematicians (algebra peeps) seem to like the classic "root 2 is irrational" proof more.)