Numbers Theory # 2; Or, How I Won a Bar Bet. Plus, a Mystery.
Well, hmmm, the thing with the infinite half distances is called Zenos paradox. The mathematical solution/explanation of/to Zeno´s paradox is taking the limit of ex. x approaching value y.
How come you did not know division by 0 was undefined, but know Zeno´s paradox?
I think you are probably looking for input from a historian/philologist/sociologist/psychologist here, but for know I shall suffice.
From my perspective "our" whole numbers are the only ones that make intuitive sense, are called real numbers for a reason. To take a prime (ary school) example here, if you hold an apple in your hands you are holding one unit. Half it, you are holding half a unit, but not a whole. So, I hear you ask, why cant we use half an apple as a baseline? It is absolutely not intuitive, you would have to describe the single apple as two apples, and while that might still make some qualitative sense come back to zenos paradox. Suddenly you are holding infinitely many apples. Similar holds true for any other decimal baseline. Why your baseline cant be 1 is obvious and hence left to the reader to consider.
Hope my logic makes some sense.