> Pi is indeterminent and thus cannot be an object to be counted
this seems weird to me. doesn't pi (the symbol) point to one specific concept, whether or not we can determine its exact shape?
this seems weird to me. doesn't pi (the symbol) point to one specific concept, whether or not we can determine its exact shape?
It is a subtle distinction but important. We define the exact value based on the context. If I am tiling my circular patio then 3.14 is fine to calculate how many tiles I need. If I going to the moon or mars then I need more decimals or I will miss the target.
The imaginary number i=SQRT[-1] is the base solution to the polynomial equation -y= x^2. If you read the history it was invented to solve certain types of cubic equations, i.e. as a heuristic of method. So not only is it not a number it is a bare contradiction. While i was useful to solve some subclass of all cubics it did not lead to a general solution to cubic equations. Nevertheless the mathematicians ran with it and added complex numbers to the definition of number so that the number system could solve all possible polynomial equations.
In my opinion imaginary numbers are a kludge and deadend and it is masking the real issues in math, i.e. the ghosts of departed quantities. In math some symbols stand for an infinite series but you can't just choose any arbitrary series for Pi or e or SQRT[2], they all have to be defined as part of a system of measurement with clearly defined and globally defined epsilon/delta (i.e. precision) of measurement to get valid results.