Originally posted by fearlessleader
unrelated, but posted for similer reasons:
in this thread:
we determined that 0\0 can take on any one real value for any one situation.
but can it take on an unreal value?
What is your definition of the operation denoted by / ?
If it represents division, what is your definition of division?
A typical definition of division is this:
For real numbers w, x, y, and z,
w/x = y/z if and only if z*w = x*y
Now, you define your function as f(x) = f(x)/1 = x/0. From this and the definition of division, it follows that you also have 0*f(x) = 1*x. By the rules of multiplication, it follows that you also have 0 = x.
That is, your function is only defined at one point, namely 0. For any other point, f cannot be defined, for if it were, its own definition would be a contradiction.
But what use is a function whose domain is a single point?