Absolute infinity: Difference between revisions
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RhubarbJayde (talk | contribs) (Created page with "Absolute infinity was a concept originally defined by Georg Cantor, the founder of set theory. He denoted it \(\tav\) and defined it as a number greater than everything else, so large that any property it could have would already be satisfied by something smaller. This is clearly not well-defined, since "being absolute infinity" is a property that it and only it has - this is similar to Berry's paradox. However, this idea paved the way for Reflection principle|reflecti...") |
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Absolute infinity was a concept originally defined by Georg Cantor, the founder of set theory. He denoted it
Absolute infinity and attempts to define numbers beyond (which is ironic, since the whole point of absolute infinity is that it could not be transcended beyond) feature prominently in fictional googology.
==As justification for reflection==
Later authors have connected Cantor's remark that absolute infinity "can not be conceived" to reflection principles. For example, Maddy states:<ref>P. Maddy, "[https://www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms1.pdf Believing the Axioms I]". Journal of Symbolic Logic, vol. 53, no. 2 (1988), pp.481--511.</ref><sup>p.503</sup>
: Hallet ... traces ''reflection'' to Cantor's theory that the sequence of all transfinite numbers is absolutely infinite, like God. As such, it is incomprehensible to the finite human mind, not subject to mathematical manipulation. Thus nothing we can say about it, no theory or description, could single it out; in other words, anything true of \( V \) is already true of some [\( V_\alpha \)].
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