Re: How many different unit fractions are lessorequal than all unit fractions?

On 9/2/24 1:07 PM, WM wrote:

How many different unit fractions are lessorequal than all unit fractions? The correct answer is: one unit fraction. If you claim more than one (two or three or infintely many), then these more must be equal. But different unit fractions are different and not equal to each other.
 Another answer is that no unit fraction is lessorequal than all unit fractions. That means the function NUF(x)
Number of UnitFractions between 0 and x > 0
with NUF(0) = 0 will never increase but stay at 0. There are no unit fractions existing at all.
 Therefore there is only the one correct answer given above.
 Regards, WM
 

Nope, because there does not exist AHY unit fraction that is less than or equal to ALL Unit fractions, as any unit fraction you might claim to be that one has a unit fraction smaller than itself, so it wasn't the smallest.
The problem with your NUF, is that it is trying to count something from and uncountable end, one that doesn't actually have an end.
Thus, if we try to find a value of y such that y = NUF(x) where x is > 0 but also a finite value, we find that such NUF doesn't exist, because it has an essentially inconsistant definition.
Your logic that tries to make it valid has just blown up your mind into smithereens.