On Monday, October 2, 2017 at 6:41:47 PM UTC-6, mitchr...@gmail.com wrote:
> Math is going forward to a simplified new.
It is true that the original concept of numbers was to answer the question "How many?", and while you can have three of something, or none of that same thing, you can't really have a negative quantity of anything - only a quantity of some different thing which, in some sense, is opposite to the original thing.
So a debt of one dollar is not the exact opposite of a dollar bill.
However, in areas where the concept of negative numbers is still useful, nothing is made simpler - things just become more complicated and awkward - if we give up negative numbers and the ability to do arithmetic with them.
Saying that for clarity mathematicians should admit that complex numbers *and even negative numbers* aren't unproblematically part of the original concept of number, but are instead extensions to that concept *is valid*; expecting these extensions to be dispensed with is not.