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fom
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Re: Matheology § 254
Posted:
Apr 18, 2013 4:40 PM


On 4/18/2013 2:42 PM, WM wrote: > > Matheology § 254 > > 1. Finite cannot comprehend, contain, the Infinite.  Yet an inch > or minute, say, are finites, and are divisible ad infinitum, that is, > their terminated division incogitable.
Yes. And how did modern mathematics characterize that?
In general, differentiablity requires neighborhoods.
Differentiability implies continuity.
Continuity is an invariant distinguishing the geometric from the arithmetic. Dimension is preserved with respect to continuous functions but not general functions.
> 2. Infinite cannot be terminated or begun.  Yet eternity ab ante > ends now; and eternity a post begins now. So apply to Space.
Yes. And how did modern mathematics characterize that?
Onesided limits.
> 3. There cannot be two infinite maxima.  Yet eternity ab ante and > a post are two infinite maxima of time.
Yes. And how did modern mathematics characterize that?
First, there is the characterizations of spaces that can be given onepoint compactifications.
Next, the nature of unbounded sequences could be analyzed and differentiated to recognize strict monotone increasing sequences and strict monotone decreasing sequences and alternating sequences strictly increasing absolutely.
A characterization of spaces respecting those sequences naturally followed (more precisely, the use of extended real numbers received a mathematical explanation)
> 4. Infinite maximum if cut in two, the halves cannot be each > infinite, for nothing can be greater than infinite, and thus they > could not be parts; nor finite, for thus two finite halves would make > an infinite whole.
Yes. And how did modern mathematics characterize that?
When attempting to arithmetically represent geometric completeness, it became clear that talk of 'infinity' could only be done with respect to 'absolute infinity' to which the above still applies.
> 5. What contains infinite quantities (extensions, protensions, > intensions) cannot be passed through,  come to an end. An inch, a > minute, a degree contains these; ergo, &c. Take a minute. This > contains an infinitude of protended quantities, which must follow one > after another; but an infinite series of successive protensions can, > ex termino, never be ended; ergo, &c.
Yes. And how did modern mathematics characterize that?
In spite of the incomprehensible language given without the historical context, this appears to involve the definition of a limit relative to the distinction of removable discontinuities.
There are some finish lines that Zeno cannot cross depending on the rules.
> 6. An infinite maximum cannot but be allinclusive. Time ab ante > and a post infinite and exclusive of each other; ergo, &c.
Mathematics actually has characterizations for this. But, this is an empirical question.
Scale relativity treats space as nondifferentiable on small scales. Time symmetry is broken at these scales in this theory.
But, mathematics has the topologies should this ever be accepted as the correct theory.
> 7. An infinite number of quantities must make up either an infinite > or a finite whole. I. The former.  But an inch, a minute, a degree, > contain each an infinite number of quantities; therefore an inch, a > minute, a degree, are each infinite wholes; which is absurd. II. The > latter.  An infinite number of quantities would thus make up a finite > quantity, which is equally absurd.
Yes. And isn't everybody happy that modern mathematics has a framework that appears to have eliminated much that is involved with this kind of absurdity?



