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In theory in the least, humans are supposed to reason things based on a universal logical thinking.
Actually, I have noticed that also logic, as everything else in the universe, is relative to the observer (to the person in question).
But this doesn’t imply that the number of human logics is equal to the number of humans on earth ![]()
Let me start with a practical example:
On my side, I don’t mind accepting a notion about something which is not real if it (as a tool) helps me discover the world better.
So when I started learning geometry, I didn’t object using in my studies the unreal object called “the geometrical dot” which has no dimensions by definition. Also I accepted to work with straight lines while their two ends at infinity are out of reach in my real world. And thanks to the notion of the basic imaginary number (i or j) whose square is -1, many problems of real projects could be solved faster and easier.
On the other hand, I usually don’t believe an idea or story (made public) as being real and true just because some other people (even in billions) do. It has to pass my logical reasoning first in order to add it in my set of knowledge.
Do all humans (mature adults) on earth have a set of knowledge close to mine? I doubt though they are not less intelligent than I.
For instance, I, unlike most people, apply the "same" processes of logical reasoning in all my studies which could be related to my human living flesh (science), my human living soul (spirituality) and the real world (mainly its hidden truths); the world as it is on the ground, far from history, the great speeches and the news.
With time, my various studies have helped me understand better how and why humans have to be different; starting from their different main priorities in life that suit best the deep nature of which they are created.
Please notice that, after all I said, it is just me... and my logic ![]()
Kerim
If a = 2, b = 1, c = 4, then A = √(2+1·√ 4) = 2, B = √(2−1·√ 4) = 0, S = A + B = 2 ≠ b.
Good work.
In this case, the original statement should be updated as:
"If their sum A+B=S comes out as a natural number, S equals b if b ≠ 1".
Thank you.
Added:
also a ≠ 0, b ≠ 0 and c ≠ 0
We have the two algebraic expressions A and B:
A= SQRT[ a + b*SQRT(c) ] and B= SQRT[ a - b*SQRT(c) ]
If “a”, “b” and “c” are natural numbers (positive integers), A and B will likely be real numbers, not natural ones.
But if their sum A+B=S comes out as a natural number, S equals “b” always.
First, I wonder if there is even one set of “a”, “b and “c” (natural numbers) that lets S be a natural number as well but not equal to “b”.
I personally couldn't find it.
Second, in case S=b (as it is supposed to be), the 3 numbers satisfy the relation c = a – b^2/4.
For example, if a=19 and b=8, c=3 (and S=b=8).
This is an example about how the sum of two non-finite decimal numbers (as A and B here) could be a nice integer.
Kerim
Hello everybody,
I am about 70. Math is my favourite since I was a kid (calculus in early years).
It happens that the process of logical thinking gives me always the greatest pleasure. So I am fortunate that my brain keeps working
though not as it used doing when I was rather young.
Obviously, math has helped me at work, since graduation (many decades ago), as a private designer (hardware and firmware) of various electronic controllers (needed by the local market/consumers).
It is nice having the chance to meet new friends who also like math.
Wish the best for all,
Kerim