(September 14, 2018 at 8:58 am)RoadRunner79 Wrote:(September 14, 2018 at 8:34 am)polymath257 Wrote: No, I *am* saying the number is subjective: it does depend on the observer and their biases.
But, more importantly, the actual identity of the number 4 is not agreed upon. Is it the set {{{{}}}}? Or is it the set {0,1,2,3}, where 3={0,1,2}, 2={0,1}, 1={0}, and 0={}?
Or do we use the notion in the integers (equivalence classes of order pairs of natural numbers)? Or in the rational numbers (equivalence classes of order pairs of integers)? Or in the real numbers (Dedekind cuts? equivalence classes of Cauchy sequences?)? Or maybe in the complex numbers (ordered pairs of real number? Or the algebraic quotient field obtained from real polynomials after modding out by x^2 +1?)
Or do we simply mean SSSS0 in an inductive set with first element 0 and successor function S (in which case, there are many, many, many different specific notions)?
Or do we count in Spanish... you seem to be hung up on language again.
Ahh...but my examples are NOT just different languages. They are different fundamentally and are *all* definitions of the *number* 4 in different contexts.
I am hung up on language because mathematics *is* a language. And the number 4 is word in that language. It doesn't have an independent existence: it is a language construct. And, in math, different aspects of the language have wildly different *definitions* of the *number* 4.[/quote]