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Virgil wrote:
In article <4572510c@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
Virgil wrote:
In article <45704f2b@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
Eckard Blumschein wrote:
On 11/29/2006 6:37 PM, Bob Kolker wrote:
Tony Orlow wrote:
It has the same cardinality perhaps, but where one set contains all the
elements of another, plus more, it can rightfully be considered a
larger
set.
Not necessarily so, if it is an infinite set.
Bob Kolker
What, is it not necessarily so that it CAN rightfully be considered a
larger set, with some justification? It doesn't have a right to be
considered that way? Why? Because it contradicts theoretical
transfinitology?
Depends on one's standard of "size".
Two solids of the same surface area can have differing volumes because
different qualities of the sets of points that form them are being
measured.
Absolutely true. I agree.
A formula relating the surface area s to volume v of a given scalable 3D
figure would boil down to a s=y^(2/3), given any linear unit of measure.
So is TO claiming that all sets are "scalable figures", each of which
can be scaled to every other set using some ingeneous formula.
I'm not the one claiming that everything mathematical can be captured as
a "set", remember?
Sets can have the same cardinality but different 'subsettedness' because
different qualities are being measured.
True.
You do? Do you mean that the addition of elements not already in a set
doesn't add to the size of the set in any sense?
In the subsettedness sense yes, in the cardinality sense, not
necessarily. In the sense of well-ordered subsettedness, not necessarily.
TO seems to want all measures to give the same results, regardless of
what is being measured.
Well, Virgilium, what I want, and I don't really think this is
unreasonable or even unrealistic, is to have mathematics become a single
cohesive system of knowledge, with respect to facts and rules, with
respect to measure and the real world, such that there exists no
contradiction within this "entire" "system". I guess that makes it sort
of a science, and I apologize for how distasteful that may seem to you. :)
What TO wants, TO has repeatedly shown that he not have the capacity to
get, at least in mathematics. Nor has he shown that anyone else has the
capacity to get those things, nor even that those things are worth
striving for.
Dude, you're really bumming me out. Total downer, man. You need to,
like, step off and chill, seriously, man. That was way uncalled for.
We're gonna have to talk, like, later. Totally later, dude. Later. Whew. ;)
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