How can all unit fractions be distinguished?

Erste Frage Aufrufe: 216     Aktiv: 04.03.2023 um 19:14

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Every natural number n has 0 larger successors. Likewise every unit fraction 1/n has smaller successors. Therefore we can define a function called NUF(x) describing the Number of Unit Fractions between x and 0:
NUF(x)=0 for x>0
NUF(x)=0 for x≤0
Acording to this function almost all unit fractions vanish in one point between 0 and (0,x). That means they cannot be distinguished.

But there must be a mistake, because all unit fractions are separated by finite distances, each one consisting of 0 fractions and further real numbers. Therefore 00 points must vanish in one point which is impossible. Can this be understood and explained?

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