My sig says IF 0/0=1. (which is false of course)
Anyways my algebra teacher once told the class that if he has 3 heads, then every student will fail. He said that's actually true, and it involves pretty deep philosophy.
Now saying 0/0=1 is assuming that you CAN divide by zero, only if the numerator is also 0.
Take x and y to be two real numbers.
You can say 0/0 = 0/0, because both sides are equal to one.
As we know, if x is any real number, then (x times 0) = 0.
So we can substitute 0 by (x times 0), and do the same for y.
Now we have (x times 0)/0 = (y times 0)/0.
Or, written differently, x times (0/0) = y times (0/0)
Substitute (0/0) for 1 to get: x times 1 = y times 1, or x=y.
x and y were just any 2 real numbers, therefore x = y for any real numbers x and y.
If someone unequivocally disproves my signature, I say he's pretty &^#*ing smart, and I'll
him or her.
Yeah, I'm gonna change my sig from 'rational' to 'real' now. sx is awesome.