Re: how

On 6/18/2024 4:47 PM, Moebius wrote:

Am 19.06.2024 um 01:18 schrieb Chris M. Thomasson:

On 6/18/2024 3:45 PM, Moebius wrote:

Am 19.06.2024 um 00:21 schrieb Chris M. Thomasson:
>
Your "approach" will work "out of the box" in physics:

[...]
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:^)
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Then I think of where:
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a = 1/2 + 1/2 = 1
b = 1/4 + 1/4 + 1/2 = 1
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a = b = 1
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Then, think of b being the complex number:
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b = 1+0i
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a = b = 1
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but a is unit fractions and b is a complex number.
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They are equal as in able to be plotted in the same place on the real line [in the coplex plane], but use different means to get to the same number?
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Fair enough?

 Yeah. As we say, the unit fractions are "embedded" (in a certain sense, don't ask) in the rational numbers, the rational numbers are "embedded" in the real numbers and the real numbers are "embedded" in the complex numbers.
 After this "embedding" the statement
       {1/n : n e IN} c Q c IR c C
 can be considered "literally true".
 For example, then the number x e IR
       such that for all numbers x' e IR: x*x' = x'
 is actually identical with the number z e C
       such that for all numbers z' e C: z*z' = z'.
 So (then) there's no difference between the 1 e IR and the 1+0i e C.
 Makes things simpler. :-P
 Wikipedia: "A real number a can be regarded as a complex number a + 0i, whose imaginary part is 0."
 (Things are slightly more complicated here, from a technical point of view.) :-P
 

Each unit fraction is a real number, but not all real numbers are unit fractions... Fair enough? ;^)