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Abner's Dream: Hyperreals

April 25, 2008

...instead of the epsilon-delta formulation, we use the HYPERREALS to create the calculus, for they contain elements which are infinitely large and small. But in order to preserve the continuity of the hyperreal line there needs to be an additional ultrafilter on top of the hyperreals... And even after we construct the ultrafilter for hyper-hyperreality, we must preserve the continuity of the new dimension...

Are you saying that we face an infinite regression here?

Indeed. Perhaps we need to consider here a union of all of the ultrafilters - for each level above the reals.

What happens then, on day omega? Can we stop there?

Why, of course, doctor. It is, after all, the final day. On the final day we will know the ANSWERS to our QUESTIONS, and the TRUTH we are seeking will become as clear as DAY. Only when we understand reality on a metaphysical level will we ever be able to grasp the mechanics of the universe...

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