Like the number PI, whose digits are an infinite sequence, the infinite-length nature of PI is inevitable because it has an infinitary quality that is not otherwise able to be represented by humans with full consistency.

The current, orthodox, math and scientific viewpoint is that it is not only o.k., but requisite to exclude traditional numbers of infinite-length to the left of the decimal point, while it is considered acceptable to admit traditional numbers like PI that are of infinite-length to the right of the decimal point.

This seems possibly to stem from a desire to have “finitary decidability”, yet why should we be able to decide something with finite vocabulary if the thing has infinite complexity? Anthropomorphizing logic (by which I mean conforming logic to what humans can argue with finitary decidability) leaves beyond consistent discussion the full representation of any infinitary phenomena.

We actually do fine with PI without full representation of its infinitary nature, because getting just a few digits provides practical computational utility (we get close enough to the answer). But other cases of finitary UNdecidability crop up for which there is no acceptable approximation (whenever the finitary undecidability involves infinite extents of numbers to the left of the decimal point).

Thank you, Ezra, for grasping and sharing the essence of the conclusion of my paper so succinctly.

It seems important to emphasize that this conclusion is not merely an assertion, but that the conclusion is actually proved with specificity of argument in my paper. Hopefully this error (and correction) at the foundations of maths and human logic can be spread broadly — and soon — so that the work of scientists may no longer rest on an over-stepping of what is possible to state with consistency in maths!

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