Re: Galileo's Paradox

In article <457af7ba$1@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Virgil wrote:
In article <MPG.1fe4233fd1946032989a0c@xxxxxxxxxxxx>,
David Marcus <DavidMarcus@xxxxxxxxxxxxxx> wrote:

Tony Orlow wrote:
Okay, a "potential" infinite set is one where each element, like the
naturals, has a specific string associated with it, which has a
left-hand end.
What do you mean "a specific string associated with it", and what is a
"left-hand end"?

If TO means a string having a first character but not a last one, the
set of all such is uncountable, so cannot represent a merely
"potentially infinite" set.

I mean a finite string.

Finite strings are alleged to have TWO ends, a lef-hand end AND a
right-hand end, so merely specifying that a string has a "left-hand end"
does not indicate that it must be finite.

By a specific string, I mean one which differs
from all other strings in the language in at least one position.

Countably infinite means potentially infinite.

What does "potentially infinite" mean to TO?

I do not know of any mathematical system in which any of the
pseudo-definitions of "potentially infinite" so far presented here make
any sense.
.

Relevant Pages

  • Re: Galileos Paradox
    ... David Marcus wrote: ... "left-hand end"? ... If TO means a string having a first character but not a last one, ... Countably infinite means potentially infinite. ...
    (sci.math)
  • Re: Galileos Paradox
    ... David Marcus wrote: ... What do you mean "a specific string associated with it", and what is a "left-hand end"? ... If TO means a string having a first character but not a last one, the set of all such is uncountable, so cannot represent a merely "potentially infinite" set. ...
    (sci.math)
  • Re: Galileos Paradox
    ... naturals, has a specific string associated with it, which has a left-hand end. ... What do you mean "a specific string associated with it", and what is a "left-hand end"? ... If TO means a string having a first character but not a last one, the set of all such is uncountable, so cannot represent a merely "potentially infinite" set. ...
    (sci.math)
  • Re: An uncountable countable set
    ... repeating decimals, ... that is every digit in that string is in a finite position with respect ... finite strings you call naturals. ... mind that the set of such finite string representations of infinite ...
    (sci.math)
  • Re: Entropy
    ... I think one can relate it to LZ, which is a fixed size "machine", who's "instruction set" are length/offset pairs, you may search for the optimal parameter-set giving the smallest output. ... you can come up with reasonable results that are of interest of the field, but you shouldn't expect to find a program that provides you with the KC of a given string. ... It contradicts sort of the universality of KC. ... And as he said, if you look to eliminate the machine dependency, you marginalize it (you don't want to consider all machines, because then you have to look infinite time on infinite machines for a finite string, that's even worst). ...
    (comp.compression)