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

On 9/2/24 4:37 PM, WM wrote:

On 02.09.2024 19:19, Richard Damon wrote:

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.
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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.
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Therefore there is only the one correct answer given above.
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Nope, because there does not exist AHY unit fraction that is less than or equal to ALL Unit fractions,

 Impossible because then NUF will never increase. Then there are no unit fractions.

Which just shows the error in the "definition" of NUF.

 

as any unit fraction you might claim to be that one has a unit fraction smaller than itself, so it wasn't the smallest.

 Your argument stems from visible unit fractions but becomes invalid in the dark domain.

But all the unit fractions are visible. You agreed to that you self as you said if n is visible, so will be n+1.
Thus, there is no smallest visible unit fraction as there can't be a last one.

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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.

 The unit fractions end before zero.

No, they don't end, they have a bound that is outside of themselves, but have no final member.

 Regards, WM