(07-27-2015 08:53 PM)georgewebb Wrote: (07-27-2015 05:41 PM)Seventyniner Wrote: Argh, that Siri 0/0 thing irritates the mathematician in me. That is to say, it irritates all of me. 0/0 isn't undefined, it's indeterminate.
I see your point, but it strikes me that the distinction between "indeterminate" and "undefined" is more than a little esoteric -- and I'm a guy who likes and respects esoterica.
George, you're a lover of precision in language, so let's take a moment to look at what those words mean and how they relate to division - I think you might change your tune.
When we divide two numbers to get a result (quotient), what are we really doing? It's the inverse of multiplication; to say that a/b = x is to say that b*x = a. That is, we're saying "What number x must we multiply by b in order to get a?"
So why is dividing a nonzero number by zero undefined? There is no solution. You can't divide 3 by 0 because there's no number you can multiply by 0 to get 3. In equations, you'd say that 3/0 is undefined because if 3/0 = x, then 0*x = 3 and there's no finite value of x that can make that true.
Dividing zero by zero is a completely different story. It's not that there's no solution, it's that
every number could be the solution! The value of 0/0 is indeterminate because if 0/0 = x, then 0*x=0, and that's true for every finite value of x!
Informally, think of it this way: "undefined" means the solution does not exist. "Indeterminate" means the solution cannot be identified. Big difference.