Re: Calculus XOR Probability

Dik T. Winter wrote:
In article <1144959368.304033.270220@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> Han.deBruijn@xxxxxxxxxxxxxx writes:
...
> Whoa, Tony, not so fast!

What I am wondering is the way you side on occasion with Tony. Your
argument appears to be that infinite sets are actually finite but
extremely large. I do not think that is what Tony is stating.

I think if you abstract away the ill-defined terminology, you find that
they are saying similar things. I'll coin the term "Thick" (of a number
for example), standing for the "Tony-Han I-word-related
Concept-Koncept". Both seem to think that if you go far enough along
the real line, numbers eventually become Thick. Han explicitly talks
about engineering/physics, in which it is true that "infinity" is used
as an approximation. For example, a lens focussed at infinity is
assumed to provide a sharp image for anything sufficiently far away. In
optical theory, for the subject to be at infinity means that the light
rays which will form a single point in the image are parallel. Thus one
diagnostic question to ask both Tony and Han is whether in R^3
(mathematical Euclidean 3D space) there are points from which rays
arrive parallel. One could also ask whether there are points with
infinite coordinate values, but I do not think this question will
elicit useful answers, because the answer will actually be to the
question "Are there Thick points?" The difference between the T and H
answers may be that Tony uses the i-word to describe them, while Han is
more keen to accept that Thick is just some sort of engineering
approximation. (Tony's stuff about "infinitesimal scale" and suchlike
terminology is another pointer to his ideas being merely about
approximations.)

Brian Chandler
http://imaginatorium.org

.

Relevant Pages

  • Re: abundance of irrationals!)
    ... Are you so friendely to others who don't agree with you Tony with your smiles. ... > You only state there's infinity in the naturals. ... And they sleep a night but the next day a new flock is arriving at the hotel doors. ... It's a complete other subject in pure mathematics. ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... What I am wondering is the way you side on occasion with Tony. ... the real line, numbers eventually become Thick. ... as an approximation. ... a lens focussed at infinity is ...
    (sci.math)
  • Re: abundance of irrationals!)
    ... Are you so friendely to others who don't agree with you Tony with your smiles. ... You only state there's infinity in the naturals. ... And they sleep a night but the next day a new flock is arriving at the hotel doors. ... It's a complete other subject in pure mathematics. ...
    (sci.math)
  • Re: abundance of irrationals!)
    ... > who don't agree with you Tony with your smiles. ... > so with the same cardinality. ... >> You only state there's infinity in the naturals. ... Mathematics is for clarifying not for obscuring things. ...
    (sci.math)
  • Re: An uncountable countable set
    ... straight line segment approximations. ... The trichotomy or real quantity itself defines a linear order. ... No but that only applies to linear approximations for pi, Tony. ... that there can be no plus or minus infinity and no continuity. ...
    (sci.math)