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Topic: How many fake unreal numbers are there in mathematics?
Replies: 28   Last Post: Dec 6, 2017 1:56 PM

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 bassam king karzeddin Posts: 2,182 Registered: 8/22/16
How many fake unreal numbers are there in mathematics?
Posted: Dec 24, 2016 12:09 PM

How many fake unreal numbers this perpetual, absolutely true and self proved inequality in mathematics would show immediately?

The famous inequality:

Iff: (m^q < p*10^{nq} < (m + 1)^q), where (q , p) are prime numbers, (n ) is positive integer, then (m) must represent the arithmetical integer of the (q?th) root of (p), ($\sqrt[q]{p}$), with (n) number of accurate digits (after the decimal notation in 10base number system)
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Example, what are the accurate five digits after the decimal notation of cubic root of say (7)

Solution, here we simply have (n = 5, p = 7, q = 3), then, apply in the above inequality as this:

What is the largest cube number (m^3 < 7*(10)^{5*3}), then (m = 191293)

A- The case of (q) is odd prime number

However this can be so simply generalized to any number system we adopt, where this can be written in Diophantine solvable equation forms by adding a significant integer function f(n,m,p,q) to our original unsolvable equation (in rational numbers), where clearly the significant function grows indefinitely for large number of digits required, which finally shows clearly the (q?th) root of any (p) is so fake legendary and unreal number in mathematics, that must be thrown out immediately from being adopted as real number.

However to see this so clearly, you would require advanced programs for more digits finding, then a complete collapse you would notice when you observe the indefinite growing of f(n,m,p,k)

So, solve the following Diophantine eqn. from this inequality, where the largest (q?th) power of (m)

(m^q < p*(10^{qn}), or

(m^q + f(n, m, p, q) = p*(10^{qn})

B- the peculiar case when (q = 2), the sqrt(p) is simply constructed from the Pythagoras theorem as a real existing number being only as a diagonal of constructible rectangle sides, as a length on a straight line (same as number line), where its endless rational representation is then obvious fake nonexistent number that tries always and hopelessly to replace the unique irrational number position on the number line of sqrt(p) constructed length, where this is so clear from the same famous inequality

There is nothing better than the true meaning of non existence of solution to some unsolvable Diophantine equations in order to simply understand what is the real number,

And when the so elementary proof of Fermat?s last theorem is revealed, then so large part of fake mathematics would be thrown out immediately!

Regards
Bassam King Karzeddin
24th, Dec., 2016