Discussion
Started 16th Dec, 2022
  • Planalto Research

Can irrational numbers be calculated in algebra?

Irrational numbers are uncomputable with probability one. In that sense, numerical, they do not belong to nature. Animals cannot calculate it, nor humans, nor machines.
But algebra can deal with irrational numbers. Algebra deals with unknowns and indeterminates, exactly.
This would mean that a simple bee or fish can do algebra? No, this means, given the simple expression of their brains, that a higher entity is able to command them to do algebra. The same for humans and machines. We must be able also to do quantum computing, and beyond, also that way.
Thus, no one (animals, humans, extraterrestrials in the NASA search, and machines) is limited by their expressions, and all obey a higher entity, commanding through a network from the top down -- which entity we call God, and Jesus called Father.
This means that God holds all the dice. That also means that we can learn by mimicking nature. Even a wasp can teach us the medicinal properties of a passion fruit flower to lower aggression. Animals, no surprise, can self-medicate, knowing no biology or chemistry.
There is, then, no “personal” sense of algebra. It just is a combination of arithmetic operations.There is no “algebra in my sense” -- there is only one sense, the one mathematical sense that has made sense physically, for ages. I do not feel free to change it, and did not.
But we can reveal new facets of it. In that, we have already revealed several exact algebraic expressions for irrational numbers. Of course, the task is not even enumerable, but it is worth compiling, for the weary traveler. Any suggestions are welcome.

Most recent answer

24th Jan, 2023
Ed Gerck
Planalto Research
The comments above show how following the RG ToS is necessary for a scientific conversation.
But the legal responsibility of enforcing the RG ToS falls only on RG, per EU law.
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Popular replies (1)

16th Dec, 2022
Ed Gerck
Planalto Research
We need to be optimistic, because that is the lesson from nature. An animal can self-medicate, obeying natural laws in chemistry that are unknown to animals. A tree grows when pruned, so we can see this pandemic as an opportunity. Let's grow, nature is not a zero-sum game!
Irrational numbers and mathematical real-numbers are uncomputable, with probability 1.
But irrational numbers can be calculated exactly in algebra and that is how animals are able to calculate-- in a network of thoughts, which does not have to hierarchical!
It can exist as an ontology, like the Internet. We, then, have to he mindful who we connect to. We can always connect to "DNS" to get the correct directions, or to a rogue DNS, of an attacker...
4 Recommendations

All replies (5)

16th Dec, 2022
Ed Gerck
Planalto Research
Examples using algebra (all results are exact):
√2 = 2.sin(45 degrees)
log(√(a/b)) = 1/2.(log a - log b)
log(√3) = 1/2.log 3
√x.√x = x
((√2)^√2)^√2 = 2
i^i= e^(-45 degrees)
π (+ k.2π)= 2×arcsin(1) (+ k.2π) -- k in the set N.
...
16th Dec, 2022
Ed Gerck
Planalto Research
Intellectual work by humans is very inspiring, but Physics knows that nature is at least 13.8 billion years ahead of us, and there might be other universes still older.
There just was not a single Big-Bang -- if one can happen, more can happen ... We might be late-comers on a feeric Tohu-wa-bohu. Evolution is a very long road.
Infinity is lame to algebra, not unknown and not indeterminate. But it is not a number, so there are no arithmetic rules to multiply/divide or add/subtract it to 1 or any number. We know that 0.x = 0, where x is a number.
2 Recommendations
16th Dec, 2022
Ed Gerck
Planalto Research
We need to be optimistic, because that is the lesson from nature. An animal can self-medicate, obeying natural laws in chemistry that are unknown to animals. A tree grows when pruned, so we can see this pandemic as an opportunity. Let's grow, nature is not a zero-sum game!
Irrational numbers and mathematical real-numbers are uncomputable, with probability 1.
But irrational numbers can be calculated exactly in algebra and that is how animals are able to calculate-- in a network of thoughts, which does not have to hierarchical!
It can exist as an ontology, like the Internet. We, then, have to he mindful who we connect to. We can always connect to "DNS" to get the correct directions, or to a rogue DNS, of an attacker...
4 Recommendations
17th Dec, 2022
Ed Gerck
Planalto Research
Since the 17/19th centuries, “the differential and integral calculus is based upon two concepts of outstanding importance, apart from the concept of number, namely, the concept of function and the concept of limit.” according to the well-known textbook by R. Courant in Germany and worldwide.
Without including any philosophical opinions, the system of rational and irrational numbers build a continuum of numbers, such that each point on an axis corresponds to just one number, and each number corresponds to just one point on the axis, called the system of mathematical real numbers(MRN).
Therefore, all MRN in the number line can be separated into one of two sets — the rationals (expressible as the ratio of two integers), and the irrationals (all the remaining MRN, which are, thus, not rationals). Every MRN is one of either. This construction is often credited to Richard Dedekind in ETH Zurich, in 1888, writing, “Numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things.”
Because uncountably infinite sets are always larger than countably infinite sets, one can conclude that there are more irrational numbers than rational ones. It is worth mentioning that the rationals and the irrationals are both dense, but unlike the rationals, the irrationals are not “sparse” and do not have zero measure mathematically.
This fact emphasizes that rationals and irrationals are really quite different -- even though one can find a rational between any two irrationals, actually an infinite number of them, and an irrational between anytwo rationals.
See more at "Algorithms for quantum computation: the derivatives of discontinuous functions", available at:
2 Recommendations
24th Jan, 2023
Ed Gerck
Planalto Research
The comments above show how following the RG ToS is necessary for a scientific conversation.
But the legal responsibility of enforcing the RG ToS falls only on RG, per EU law.
Meawhile, it is suggested to read the question text, with the latest references. Also, private messaging is available.

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Irrationals solved in algebra?
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57 replies
  • Ed GerckEd Gerck
Our answer is YES. Irrationals, since the ancient Greeks, have had a "murky" reputation. We cannot measure physically any irrational, as one would require infinite precision, and time. One would soon exhaust all the atoms in the universe, and still not be able to count one irrational.
The set of all irrationals does not even have a name, because there seems to be no test that could indicate if a member belongs to the set or not. All we seem to know is it is not a rational number -- but what is it?
There, Instead of going into complicated values of elliptic curves, and infinite irrationals, algebra allows us to talk about "x".
No approximating rational numbers need to be used, nor Hurwitz Theorem.
Thus, one can "tame" irrationals by algebra, with 0 (zero) error. For example, we know the value of pi. It is 2×arcsin(1) exactly, and we can calculate it using Hurwitz Theorem, approximately.
GENERALIZATION: Any irrational number is some function f(x), where x belongs to the sets Z, or Q -- well-defined, isolated, and surrounded by a region of "nothingness". The set of all such numbers we call "E", for Exact. It is an infinite set.
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  • Jean-Claude EvardJean-Claude Evard
=====================================
See also my list of links to my other RG documents:
=====================================
Question posted on May 20, 2018
Are there other pieces of information about “Victory Road” to FLT?
I have posted a research project on Research Gate on the history of the construction of “Victory Road” to the proof of Fermat Last Theorem (FLT).
Are there pieces of information that are missing in this history?
I will add to this history any new references, pieces of information, and good comment about this history, with full credit to the first who finds it.

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