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

Ross Finlayson presented the following explanation :

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.

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Some number theorists have that there's a point at infinity
and it's natural that way.
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The first "counterexample in topology" in "Counterexamples in Topology"
is that there's a smallest non-zero iota-value.
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When there are at least three models of real numbers,
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line-reals
field-reals
signal-reals
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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.

However, if one desires to add two plus four, it is not necessary to use complex numbers as your domain and codomain just because the naturals are contained in the complex number system. This, a form of the K.I.S.S. priciple. He wants to use the reals so he can pretend that there is a smooth sweep across all values in the interval. In reality each of his values is jumped to and there are Aleph_zero of them as each is defined as next (successor function) to the previous.