Definitions for hyperstructure
hy·per·struc·ture

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1. Hyperstructure

   Hyperstructures are algebraic structures equipped with at least one multi-valued operation, called a hyperoperation. The largest classes of the hyperstructures are the ones called H v {\displaystyle Hv} – structures. A hyperoperation ( ⋆ ) {\displaystyle (\star )} on a nonempty set H {\displaystyle H} is a mapping from H × H {\displaystyle H\times H} to the nonempty power set P ∗ ( H ) {\displaystyle P^{*}\!(H)} , meaning the set of all nonempty subsets of H {\displaystyle H} , i.e. ⋆ : H × H → P ∗ ( H ) {\displaystyle \star :H\times H\to P^{*}\!(H)} ( x , y ) ↦ x ⋆ y ⊆ H . {\displaystyle \quad \ (x,y)\mapsto x\star y\subseteq H.} For A , B ⊆ H {\displaystyle A,B\subseteq H} we define A ⋆ B = ⋃ a ∈ A , b ∈ B a ⋆ b {\displaystyle A\star B=\bigcup _{a\in A,\,b\in B}a\star b} and A ⋆ x = A ⋆ { x } , {\displaystyle A\star x=A\star \{x\},\,} x ⋆ B = { x } ⋆ B . {\displaystyle x\star B=\{x\}\star B.} ( H , ⋆ ) {\displaystyle (H,\star )} is a semihypergroup if ( ⋆ ) {\displaystyle (\star )} is an associative hyperoperation, i.e. x ⋆ ( y ⋆ z ) = ( x ⋆ y ) ⋆ z {\displaystyle x\star (y\star z)=(x\star y)\star z} for all x , y , z ∈ H . {\displaystyle x,y,z\in H.} Furthermore, a hypergroup is a semihypergroup ( H , ⋆ ) {\displaystyle (H,\star )} , where the reproduction axiom is valid, i.e. a ⋆ H = H ⋆ a = H {\displaystyle a\star H=H\star a=H} for all a ∈ H . {\displaystyle a\in H.}

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1. Hyperstructure

   The hyperstructures are algebraic structures equipped with at least one multi-valued operation, called a hyperoperation. The largest classes of the hyperstructures are the ones called Hv – structures. A hyperoperation on a non-empty set H is a mapping from H × H to power set P*, i.e. : H × H → P*: → x*y ⊆ H. If Α, Β ⊆ Η then we define is a semihypergroup if is an associative hyperoperation, i.e. x* = *z, for all x,y,z of H. Furthermore, a hypergroup is a semihypergroup, where the reproduction axiom is valid, i.e. a*H = H*a = H, for all a of H.

How to pronounce hyperstructure?

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Numerology

1. Chaldean Numerology

   The numerical value of hyperstructure in Chaldean Numerology is: 2

2. Pythagorean Numerology

   The numerical value of hyperstructure in Pythagorean Numerology is: 1

References

1. ^ Wikipedia
   https://en.wikipedia.org/wiki/Hyperstructure
2. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=hyperstructure