Some Algebraic Inequalities

Dear colleagues and geometry enthusiasts,

I invite you to tackle an original aesthetic geometry problem:

Reconstruct triangle ABC using points M1, L1, and H2 (based on the diagram).

That an n degree polynomial CAN always be factored up into n factors containing Complex roots has been shown true, but there are things not explained in the phrase.

Teachers will not usualy explain alternatives.

Say (Z-x)(Z-x) =0 CAN have the solution Z=x, but can also have Z=x+ey where ee=0 is an

nilpotent element.

Just as i can be made real in 2 by 2 matrices, so can e. Just as we use i or -i dupliciously,

without knowing which, we can use e or e(T) , the transpose of e. One can define i=e-e(T)

using ee=0 , e(T) e(T) =0 and e e(T)+e(T)e =I to show ii=-1. Now substitute this everywhere you see i, and the factorization carries out the same.

Defining ww=1, one can also claim w=e +e(T).

Reading attentively the fundamental theorem of algebra, we find the funny phrase that it is not derivable from algebra...well no wonder.

Dont really have a good name for these elements, i plus whatever else there is. The supra real? Hyper real is already occupied by non standard elements. Neither have they seemingly been well studied well beyond quadratic, though they do exist...

This means a gap in knowledge? Or stuborn historical usage?

I did not understand from the author how he arrived at these specific equations ?

what is phi^1 ,phi^2 ,...

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It would be very interesting to obtain a database of responses on this question :

What are the links between Algebra & Number Theory and Physics ?

Therefore, I hope to get your answers and points of view. You can also share documents and titles related to the topic of this question.

I recently read a very interesting preprint by the mathematician and physician Matilde Marcolli : Number Theory in Physics. In this very interesting preprint, she gave several interesting relations between Number Theory and Theoretical physics. You can find this preprint on her profile.

I've been wondering because the definition of an eta-open set is if A ⊆ int(cl(int(A))) U cl(int(A)). While the semi-open set is if A ⊆ cl(int(A)). So, if int(cl(int(A))) just a subset of cl(int(A)), then int(cl(int(A))) U cl(int(A)) = cl(int(A)). This implies that an eta-open set is equivalent to a semi-open set. Can anyone enlighten me with this? because I've looking for examples that make these two sets not equivalent and still nothing found yet.

Since the generally accepted theory of gravity is GRT, one could try to derive it from some algebraic theory. The basic thing in this theory should be the Dirac algebra, in which the Minkowski space is naturally embedded. Thus, we need to find some dynamical algebra that would be locally equivalent to the Dirac algebra. Where does such a Miracle live?

Following the findings in the field of deformable algebra, can deformation of an n-dimensional vector space contribute to changing its initial dimension?

How will this contribute to finding the appropriate deformations for infinite-dimensional algebra on the basis that algebra is a vector space with an additional structure, with the hope that this will lead to new physical systems with an infinite number of symmetries, and thus complementarity in the hope of enhancing one of what the theory of strings aspires to ?