Re: Calculus XOR Probability

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

Can you provide a definition of what it means for a set C to be "a
line of some sort, with a real measure of length"?

E A (endpoints)

I don't understand your terminology. Do you mean that there exists a
function A which has as domain of some set of which "endpoints" is a
member? What is "endpoints"? Do you presume it is an arbitrary set of
pairs in R^2? What then is the value of A(endpoints)? Is it a real
number, or some other thing?

Cheers - Chas



Gee, the way you snipped that in isolation, it makes as little sense as you
make it out to. Now, go back to the original post, ...

Here is the complete block of statements you provided in response to
the question "Can you provide a definition of what it means for a set C
to be "a line of some sort, with a real measure of length"?"

E A (endpoints)
E B
E x<>A -> E y: x=successor(y)
E x<>B -> E y: y=successor(x)
x=successor(y) <-> y=predecessor(x)
Length=Sum(x=successor(A)->B: x-predecessor(x)) where subtraction of
points
indicates distance, which depends on the dimension of space.

and see if that part in
parentheses isn't a comment on those first two lines.

Why put a comment /between/ two statements "E A" and "E B", if you mean
that comment to be relevant to both lines?

Notice that 's' at the
end of "endpoint"? In English, when we append 's' to a noun, that's the usual
way we pluralize so it refers to more than one.

This isn't English. It's mathematics.

So that would be referring to
more than one endpoint, and obviously doesn't refer to just A. It's a comment,
otherwise there wouldn't be a space before the parentheses.

So by:

E A (endpoints)
E B

you meant "There exists A and B, which are endpoints".

Having determined that, what is an endpoint? What relationship does it
have to the set C, about which we are trying to determine whether or
not it is "some sort of line, with a real measure"? Are A and B members
of that set, or not neccessarily? For example, is the set {(a,b) : a =
0, 0 < b <=1}, where a and b are real numbers, a "line of some sort,
with a real measure of length"? If so, what are the endpoints A, B of
this set?

Cheers - Chas

.

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