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On 10/28/24 6:36 AM, WM wrote:
It has the value 0 for all x =< 0. And it cannot jump by more than 1 at any point.NUF increases by 1 or more, but more would violate mathematics.No, NUF(x) jumps from 0 to Aleph_0 in the domain of finite numbers, because there is no finite x where it has the value of 0.
It is just a "undefined" function.No, but the first steps happen at undefinable x.
That is true. The bottom is dark.>Note, it isn't an "infinity between" it is that the "bottom" of (0, 1] doesn't exist as a definable point.>Hint: For each and every x e IR, x <= 0: NUF(x) = 0>
and for each and every x e IR, x > 0: NUF(x) = aleph_0.
That is blatantly wrong because it would require that ℵo unit fractions exist between 0 and each and every x > 0, i.e., the open interval (0, 1].Right, like is what happens.>
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It may seem strange to a person stuck in finite logic, but is true when you understand how infinity works.
This infinity between 0 and (0, 1] is not what I can accept.
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