Re: Calculus XOR Probability

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

These facts can be deduced from the /definition/ of "limit of a
sequence of sets of points" that I gave previously.

I don''t know what you mean by "a line of some sort, with a real
measure of length", so I can't otherwise comment on whether or not your
statement is correct or incorrect; it is meaningless to me,
mathematically speaking; although as regular English usage it seems
contradicted by the example I just gave.

A disk contradicts a line? Dear god, now you sound like Lester!


So you propose that the statement "a disk is a line of some sort, with
a real measure of length" is /not/ contradicted by your definition of
"a line of some sort, with a real measure of length", when we take this
definition as being the regular English usage of that phrase?

Cheers - Chas



It's not the same thing. If I call your dog an elephant, have I proven an
inconsistency in your dog?

No, but if you say "you have an elephant in your backyard", and I say
"What the hell!!!?! Where?" and you point to my dog, we have a
disagreement about what an "elephant" is. To resolve this confusion in
the future, it is helpful to have a definition that we can agree on and
apply independently, instead of my having to ask you to literally point
at the thing you are calling "an elephant" every time you say
"elephant".

You offer a disk as an example of a line, and that's
supposed to contradict anything I said about lines?

No, read what I said. I simply asked if the statement "the disk is a
line of some sort" is contradicted by /your definition/ of "a line of
some sort". I presume the answer is "yes, because the disk is not a
line of some sort; which you can see for yourself because {insert
demonstration that a disk does not satisfy your definition of a line of
some sort}".

A disk is not a sequence of points. In a sequence, there is at most one element
before and one element after each element. In the disk, each point has an
infinite number of contiguous points, since one can move in any of an infinite
number of different directions. So, without a definition of a sequence of
locations whioch fills the 2D space, no, your disk is not a line.


If the disk fit the
definition of a line I gave, the definition would need refinement. As it
stands, I don't know what your point is.

My point is: your definition needs refinement. It does not tell me, for
example, if {(a,b): b = a^2 * sin (1/a), 0 < a < 1} is "some sort of
line" or is instead, an elephant.

It's an elephant, and a white one to boot.


Similarly, is the set {(a,b) : b = 1 - a, a,b>=0} a "line" or a
"fractal line"? You seem to believe that if I call that set by the name
"the diagonal", then it is a line, but if I call that set "the limit of
a sequence of curves", then it is a "fractal line" - even though it's
the same set in both cases.

Because I take into accout infinitesimal differences which the standard
approach ignores, I don't see that equation as accurately decribing the
staircase in the limit. I'll concoct a directed limit that allows measure, if I
must.


If I call my dog "Jumbo" is he an elephant, because "Jumbo" is the name
of an elephant?

No, and if you call your limit the diagonal, does that make it a straight line?


Cheers - Chas



--
Smiles,

Tony
.

Relevant Pages

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  • Re: Calculus XOR Probability
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  • Re: Calculus XOR Probability
    ... Distance and length are real numbers. ... It's a sequential set of points, that is a line of some sort, with a real ... A sequence of elements from some set X is essentially a function f: ...
    (sci.math)