free throws are conceptual, they are not real nor are they naturally equivalent, their equivalence are purely our creation
Free throws aren't real?
But seriously, do you honestly reject the very concept of fractions?
I mean, you want to get down to physics, consider water, in pure water, 1/3 of the atoms are oxygen.
Exactly, accurately, predictably.
I think the problem you have is not with the concept of 1/3 but with the way it is represented in the decimal system. That's a limitation of the system, it's just notation after all, I can explain to you (I think) why it makes sense for 0.333... to be equal to 1/3 (or 0.999...=1 if we really want to play that
math game) but I want to make sure we're on the same page in regards to fractions, what they are and how real are they, cause we're not going to get anywhere otherwise.