Back ... ... ... ... ... ... ... ... ... ... ... Send comments to review committee. ... ... ... ... ... ... ... ... ... ... ... Forward
The bead game is under development. The interactive function of the game comes from clicking the forward and back links above and from game players sending in Remarks. These Remarks are often edited to produce a distinct separation of concepts. Remarks edited in a way that is not faithful to the particapant's meaning can be revised. Linking in additional comments can be made via submission of beads.
E-mailed Remarks from Alex Zenkin edited into three beads (*) (This one) (*)
It is not interesting here what Cantor himself speaks and thinks on the "nature" of the actual infinity. It is important here how he really uses that notion in his "mathematical" proof.
From the point of view of the Cantor "proof", the algorithmic, operational sense of the actuality of X being infinite consists in that a given enumeration
1) contains ALL elements of some set. And only such actuality condition permits Cantor to state that the Cantor Diagonal Number y1 is different from ALL elements of the given enumeration
2) and that therefore the given enumeration does not contain ALL elements of the set X.
It is only this condition of the actuality that enabled Cantor to get the desired contradiction "not-B and B" in his "proof."
All other metaphysical interpretations of the Cantor's proof are speculative, quasi-philosophical interpretations. These interpretations need to be separated for the main force of mathematical and logical arguments.