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Post by xxxxxxxxx on Jan 31, 2019 22:31:37 GMT
The Contradictory State of Real Numbers and Completeness Fallacy of Completeness in Real Numbers "Intuitively, completeness implies that there are not any “gaps” (in Dedekind's terminology) or “missing points” in the real number line. This contrasts with the rational numbers, whose corresponding number line has a “gap” at each irrational value. In the decimal number system, completeness is equivalent to the statement that any infinite string of decimal digits is actually a decimal representation for some real number." en.wikipedia.org/wiki/Completen ... al_numbers 1. The decimal represention for some real number in itself is a rational number. 2. This necessitates a "gap" as the number of decimal points, as a rational number necessitating the real number, results in a gap between points. 3. This "gap" between points, where the point effectively act as rational number in itself, necessitates an irrational value between the points resulting in "fractal points" as a contradiction in terms. Post by Eodnhoj7 » Fri Jan 25, 2019 2:32 pm Fallacy of Completeness in Real Numbers "Intuitively, completeness implies that there are not any “gaps” (in Dedekind's terminology) or “missing points” in the real number line. This contrasts with the rational numbers, whose corresponding number line has a “gap” at each irrational value. In the decimal number system, completeness is equivalent to the statement that any infinite string of decimal digits is actually a decimal representation for some real number." en.wikipedia.org/wiki/Completen ... al_numbers 1. The decimal represention for some real number in itself is a rational number. 2. This necessitates a "gap" as the number of decimal points, as a rational number necessitating the real number, results in a gap between points. 3. This "gap" between points, where the point effectively act as rational number in itself, necessitates an irrational value between the points resulting in "fractal points" as a contradiction in terms.
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Post by Eugene 2.0 on Oct 4, 2020 18:27:03 GMT
The "gap" never appears, because the numbers mirror themselves as a background from our reality.
Real numbers are reflection to our world. Our world allows not identical identities to occur. Not identical identities fill everything that can be found as a gap.
In other words, there are always routes to fill those gaps with something.
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Post by xxxxxxxxx on Oct 5, 2020 21:32:36 GMT
The "gap" never appears, because the numbers mirror themselves as a background from our reality. Real numbers are reflection to our world. Our world allows not identical identities to occur. Not identical identities fill everything that can be found as a gap. In other words, there are always routes to fill those gaps with something. All numbers have a gap between eachother. For example 1 progressing to 2 necessitates a gap through fractions where 1 progressing to 2 observes 1.1, 1.2, 1.3, etc, occuring between them. These fractions in turn have a gap between them as well. For example 1.1 and 1.2 have the fractions of 1.11, 1.12, 1.13 occuring. These fractions in turn possess a gap between them as well with these gaps appearing respectively between the fractions which occur between them, so on and so forth. All numbers have a series of progressively occuring gaps with these gaps being irrational in themselves considering they exist continuously considering not only does one gap progress to another but simultaneously each gap is a continuum of infinite numbers as fractionsl
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