Why x*0 = x

[robvalue]

I am practically having sex with algebra, and any which-way you cut it, 0*x=0 is the only sensible and consistent result. I fully appreciate challenging any sort of ideas, and if you had a good case as for why the result should be anything different, I'd be very interested. But as it happens, you've yet to present anything convincing.

Consider any real world example where you use multiplication, and see if you can come up with a single instance where it would make any sense for 0 * X = X.

As I said, you could create a new system where the above is true, as you can define the multiplication operation to be whatever you want. Whether or not the system would be of any practical use would remain to be seen.

[Alex K]

One would surely have to give up the distributive law, and my suspcion is that if one wants to keep the most basic properties such as commutativity and uniqueness, that the * would basically become a second + if you force 0 to be the neutral element.

[robvalue]

Yes, exactly.

0*5 = (1 - 1) * 5 = 1*5 + (-1)*5 = 5 - 5 = 0

Or, in words, no piles of five is one less pile of five than one pile of five; so the result should be 5 less than one pile of five. I can't understand how pool is thinking that no piles of five works out at five.