10 Feb '05 20:28

given f(x)=(-1)^x

evaluate f'(x)

evaluate f'(x)

- Joined
- 03 Oct '03
- Moves
- 671

my head- Joined
- 03 Oct '03
- Moves
- 671

my head- Joined
- 13 Dec '04
- Moves
- 49088

Tha Brotha Hood10 Feb '05 23:341 edit

What is your definition of the operation denoted by / ?*Originally posted by fearlessleader***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?- Joined
- 04 Jul '02
- Moves
- 3790

Loughborough- Joined
- 19 Jun '04
- Moves
- 3257

at the centre