10 Feb 05
1 edit
Originally posted by fearlessleaderWhat is your definition of the operation denoted by / ?
unrelated, but posted for similer reasons:
in this thread:
http://www.redhotpawn.com/board/showthread.php?threadid=15717
we determined that 0\0 can take on any one real value for any one situation.
but can it take on an unreal value?
f(x)=x/0
evaluate.
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?
