Re: Calculus XOR Probability

cbrown@xxxxxxxxxxxxxxxxx wrote:
Tony Orlow wrote:
cbrown@xxxxxxxxxxxxxxxxx said:
Tony Orlow wrote:

<snip>

[T]echnically, yes, spaces like
lines, planes, etc, are generally defined as sets of points, and I think that's
alright, with proper metrics and such. :)

So if a function f "returns" a set of points which is the same set of
points D = {(x,y) : x+y=1, x,y >= 0}, then we don't have to "guess":
that set of points has length sqrt(2), and no other value, right?

Cheers - Chas



If the line is defined by that formula, then it is differentiable, and the
derivative is a constant -1. However, the derivative of the staircase is a
constant 0, with points of discontinuity where the derivative is infinite.

And the derivative of sin is cos. And if we look at the usual approach
curves for sin, they have discontinuities as well. So what?

It is also true that the polygon approximations of a circle all have
discontinuities. As the number of sides increases, the number of
discontinuities increases. Of course in "the limit", the number of
discontinuities is 0.

Stephen
.

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