Re: Musatov responds to WM on Cantor: intelligence, real, judge for yourself: Cantor’s idea seems to me to ass ume because two sets converge to infinity the nature of infi nity and the number of elements in each set must become equa l.
Posted:
Jun 17, 2010 8:50 PM
On Jun 17, 2:37 am, Simplane Simple Plane Simulate Plain Simple <marty.musa...@gmail.com> wrote: > COMMENTARY > To contrast my conception to my perception of Cantor?s conception of > the infinite. Cantor?s idea seems to me to assume because two sets > converge to infinity the nature of infinity and the number of elements > in each set must become equal. > Requiring one to one ?mapping? anything other than a one to one > correspondence is excluded. > My conception is more as infinite quantities are not mathematically > expressible, in the sense we can only conceive of infinity as > something consisting forever. You start with something finite and then > multiply or divide it forever. In this way two infinite sets are not > equal but, as shown in they can be ratio-ed by the finite expression > defines the set, but both extend infinitely. > Cantor?s reversal of conceptions, for some sets (non-d enumerable) > uses conception #2. This is a contradiction to conception #1, and it > would seem to me it can?t be both ways.
Musatov might be interested in knowing about Tony Orlow, who is working on a set size that is very similar to Conception #1 above.
In particular, Musatov describes how he uses ratios to determine that the size of {2,4,6,8,...} is exactly half that of {1,2,3,4,...}, since the elements of the sets are in the ratio 2:1. TO uses a similar argument to conclude that if {1,2,3,4,...} has the set size (or "Bigulosity") tav, then {2,4,6,8,...} would have a Bigulosity of tav/2.
TO uses the name "Post-Cantorian" to describe those who use what Musatov calls "Conception #1," as opposed to the "Cantorian" Conception #2. Thus, Musatov and TO are natural allies wrt set size.
On the other hand, Herc and WM are "Anti-Cantorian" in that they don't believe in different sizes of infinity. So I'm glad that Herc and WM are in this thread together. So these two reject both Conceptions #1 and #2.
If Musatov would like to learn more about TO's set size, he can click on the current TO thread (warning -- this thread now exceeds 500 posts).
