Re: How many different unit fractions are lessorequal than all unit fractions? (replete large numbers)

On 09/06/2024 03:31 PM, FromTheRafters wrote:

WM has brought this to us :

On 06.09.2024 20:17, FromTheRafters wrote:

WM submitted this idea :

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What the Hell could mean "to increase at an x" ?

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Example: The function f(x) = [x] increases at every x ∈ ℕ by 1.

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Make up your mind, is x real or natural.

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ℕ c ℝ.

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So what? There is no natural number of unit fractions less than any
positive real or natural number. You said x was real in another post and
here you claim it is natural. The output of your function is a constant
Aleph_zero not a continuum.

Some number theorists have that there's a point at infinity
and it's natural that way.
The first "counterexample in topology" in "Counterexamples in Topology"
is that there's a smallest non-zero iota-value.
When there are at least three models of real numbers,
line-reals
field-reals
signal-reals
after an Integer Continuum a la Scotists and before a
Long-Line Continuum a la duBois-Reymond, and there are
at least three law(s) of large numbers, and at least
three models of Cantor Space the square, sparse, and signal,
in a world where Vitali and Hausdorff already proved the
existence of doubling-spaces and doubling-measures before
there were Banach and Tarski, then it gets into that
"natural" is of a more replete surrounds than counting numbers.