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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) (*) (*)
Humankind, from Aristotle's' time, discusses the problems concerning the nature of potential ("mathematical") infinity versus actual ("metaphysical") infinity. But an end of these discussions isn't seen even today.
I am not sure that we are able to complete that discussion now.
Cantor himself produced a lot of texts as to potential, actual, absolute, "in concreto", "in abstracto", metaphysical, theological, etc. infinities. But all these "definitions" and their considerations are beautiful (but quite empty) words having no legitimate attitude to mathematics.
Cantor's Theorem on the uncountability of the set X of all real numbers x, belonging to the segment [0,1], is the only place where the actuality of a set X having the property of being infinite is really used as a mathematical (i.e., not philosophical) object.