>>97
Think about it this way.
It π is greater than a number A such that
Ak=k+k+k
and less than a number B such that
Bk=k+Ak
Those numbers are called "3" and "4".
Moreover, let there be a number, call it D.
Then for any real x, (4D+4D+D+D)x=x i. e. 4D+4D+D+D is the multiplicative identity.
And a number C such that 4D+4D+D+D=C.
Then π must be between 3+C+D+D+D+D and 3+C+D+D+D+D+D
It is actually very arbitrary choosing D such that ten of them add up to the multiplicative identity. Indeed, I could have chosen any other base, perhaps base-7 if I wanted to. You can call it a "whole number" if you want, but it does not change the fact that that given the additive identity (call it "0"), and the multiplicative identity (call it "1"), and using the sets 1, 1+1, 1+1+1, ..., and the set -1, -1-1, -1-1-1, ..., that π would not be found on either of the lists.
The fact is that the term "whole number" is just that: a term. It is not anything other than that, and has no meaning other than its immediate definition of:
0 is within W
If a is within W, then a+1 is within W
Or the integers can have the definition of
All elements of W is within I
If a is within W, then -1*a is within I.
And for the rationals, R, define it to be all numbers r such that there exists two numbers within I, a and b, such that
ar=b.
π cannot be found in either of the lists.
The great fault in your thinking there is that while geometry does not do much multiplication, rescaling is no problem. "1" radian or degree or "2" radians or degrees have no meaning other than assigning something to a scale. However, the real line is not a scale. The distributive property is the very important property, (a+b)c=ab+ac. This is not used for scales, but it is used for all fields.
"there should be a kind of math that treats π as a single whole number"
There is no math that treats any number as a "single whole number." First, define "single whole number." Then we'll talk.