On Saturday, July 8, 2017 at 5:30:09 PM UTC+3, bassam king karzeddin wrote:
> The exponent operation was defined earlier for positive integers, which is completely digestible and also very common sense
>
> So considering the positive integer (n), the (n = n^1), which means simply the integer (n) isn't multiplied by itself any number of times, which equals to itself only as (n)
>
> For (n^2) it simply means the integer (n) is multiplied by itself one time only as (n*n)
>
> Similarly for (n^3) which implies that the integer (n) is multiplied by itself twice as (n*n*n)
>
> So, anyone can deduce that when (k) is positive integer then the exponent operation (n^k), implies directly that is the integer (n) is multiplied by itself (k - 1) of times, very easy and not any big deal
>
> And the same can be applied by its reciprocal as n^{-3}, where this simply can be generalised to any non-zero integer and negative integers k, as n^k, where (k) is generally non-zero integer
> Up to here everything was rational thinking and very sensible, no doubt aroused and no new puzzles were added
>
> But, the time came when real irrational numbers were simply discovered with the square root operation, from the mainly lonely proved theorem (PT) in mathematics, and it was a very big event in the history of mathematics to talk about an existing number or length as sqrt(2), that was never occurring to any human mind
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> At the beginning, the square root and other sqrt(sqrt(sqrt…))) operations were adopted and were denoted only as square root operation, and never were denoted by an exponent rational number as (1/2) or (1/4) or generally 2^{- n}
>
> So, let us see indeed what does it mean to write sqrt(n) as equals n^(1/2) in accordance with above-mentioned common sense understanding?
>
> Does it mean really that the integer (n) is multiplied by itself negative half time? Wonder
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> Of course, it sounds utterly very crazy and so meaningless according to original definition of power or integer exponent clear operation
>
> But why and who was the first cheater to adopt the fraction exponent operation?
>
> Personally, I don’t know who that Big Devil was, nor I want to know, but certainly, I know why he did that guilty trick for sure?
>
> Of course, by later expanding so simply the multiplication rules of INTEGER exponents as:
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> (n^a)*(n^b) = n^{a + b}, he played the same trick for (n^{1/2})*(n^{1/2}) = n^{1/2 + 1/2} = n^1 = n, even it works accidentally here for this square root case, but the Devil aim was much dangerous and far beyond that too naïve innocent mathematician sensible thinking, especially that would please the vast majorities of them since it provides them with very easy tools to discover something very easy to play with and also gives them so many illegal chances to produce and make very easily big fake results out of nonsense
> Hence, the mathematicians had been victims, and were deceived so badly and beyond any sensible limits and also for so many long centuries for sure
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> And the true Devil had opened wide doors for many of his alike to play the same dirty games against the so innocent human minds
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> So, what was the Big Devil true aim out of this very silly and well-exposed game really?
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> He simply expanded this algebraic principle and further claimed that if (a, b) are fractional numbers where (a + b = 1), then simply (n^a)*(n^b) = n, and the way was then paved very well to establish any junk number and call it as a real existing number.
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> for instance and for the simplest case consider (a = 1/3, b = 2/3, n = 2), and Appling the Devil easy principle, then (2^{1/3})*(2^{2/3}) = 1, and of course, and almost any mathematician on earth NOWADAYS would simply find it so logical, very neat and absolutely very true, because simply he was learnt that and never would question this type of questions, on the contrary, he would keep arguing as if he had himself proved this kind of so foggy fictions
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> So, here it is so easily manufactured the cube root of two as a real number, despite this was even proven as impossible number with a few lines proof since thousands of years by the Greeks, (recall the impossibility of doubling the cube problem)
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> Some innocent argumentative would shout, yes this air thematic real number (2)^{1/3} was proven irrational number, but the fact that there isn’t any irrational number that is not constructible, and I add, it is not only not rational or not irrational, but not anything at all for sure
> It is only a notation in mind
>
> Or do you think it is that number integer (2) that is multiplied by itself a negative number of (- 2/3) times? Wonder!
> Is not that a mere obvious utter nonsense for sure?
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> However, many irrefutable published proofs available for public's freely from my posts in my both profiles and also at Quora and EMS, despite those are moderated sites and can hide and steal any issue so shamefully and so easily, but here they can’t do anything for sure
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> Of course when zero was adopted or invented and was considered to be as any real integer, even though it doesn’t have any inverse like any integer has, then the exponent zero was a matter of adoption or decision to define that (n^0) must be equal to unity, a kind of an agreement (unproven), and was based on general conclusion among old mathematicians just to facilitate and justify their later huge meaningless output in this regard as a real discovered mathematics, wonder!
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> So, the theme is that the integer is multiplied by itself a number of times which is integer number and not any other kinds of numbers
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> Is not it so strange that while the whole world of mathematics in this internet age keeping teaching more and more factions, only a few people on earth can realise that?
>
> But, almost this is the common case even from the moderated fake history of mathematics for sure
>
>
> Regards
> Bassam Karzeddin
> 8th July 2017