Right - it's not undefined if you specify the functions.
If you don't specify the functions, then f(x) itself is undefined.
I think "unknown" is more precise here. We can determine whether it is defined or not once we know what the functions actually are. If, for example, a = 0, f(x) = x, g(x) = 1/x², then we have
lim x = 0 x->0
and
lim 1/x² = ∞ x->0
however
lim[ x * (1/x²) ] = x->0
= lim 1/x x->0
which is undefined, as that limit does not exist.
So in conclusion, we need Dragon to define a, f and g to proceed.
Well there are orders of infinity so the limits are defined. To expound:
Infinity times infinity would seem to be larger than infinity. In other words it's a higher order of infinity.
And also as 0 times any number is 0 and infinity times any number is infinity it would seem there is some special relation between the concepts of zero and infinity.
This implies there must be orders of zero also. As I specified blacker than the blackest black this would imply a higher order of zero, which is to say a zero that is more zero than zero. eg: 0 times 0 like infinity times infinity.
Now as we have a higher order zero times by a lower order infinity we're going to be left with a low order zero which in this case is our good old number line zero that equates to black.
So blacker than the blackest black times infinity is really just your garden variety shade of black
Also I'd like to let the f(x) equal to a small mango...
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« Last Edit: March 10, 2009, 10:30:56 pm by Dragon »
Purple wins, but you people are crazy if you think you can keep me out of Photoshop. The purple voters did not come to an agreement on which shade of purple they wanted, so I turned purple into a magenta. Here is the result:
Every image you see other than the first one is part of an explosion animation. I made a new projectile by hand because the other one was kind of ugly.