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The first term in this sequence, the order of E 8 (2), namely 337 804 753 143 634 806 261 388 190 614 085 595 079 991 692 242 467 651 576 160 959 909 068 800 000 ≈ 3.38 × 10 74, is already larger than the size of the Monster group. This group E 8 (2) is the last one described (but without its character table) in the ATLAS of Finite Groups. [6]
The manifold can be constructed by first plumbing together disc bundles of Euler number 2 over the sphere, according to the Dynkin diagram for . This results in P E 8 {\displaystyle P_{E_{8}}} , a 4-manifold whose boundary is homeomorphic to the Poincaré homology sphere .
The number e (e = 2.71828...), also known as Euler's number, which occurs widely in mathematical analysis The number i , the imaginary unit such that i 2 = − 1 {\displaystyle i^{2}=-1} The equation is often given in the form of an expression set equal to zero, which is common practice in several areas of mathematics.
{8/4}=4{2} {8/2} or 2{4}, like Coxeter diagrams + , can be seen as the 2D equivalent of the 3D compound of cube and octahedron , + , 4D compound of tesseract and 16-cell, + and 5D compound of 5-cube and 5-orthoplex ; that is, the compound of a n-cube and cross-polytope in their respective dual positions.
E 8, an exceptional simple Lie group with root lattice of rank 8; E 8 lattice, special lattice in R 8; E 8 manifold, mathematical object with no smooth structure or topological triangulation; E 8 polytope, alternate name for the 4 21 semiregular (uniform) polytope; Elementary abelian group of order 8
The E 8 lattice is a discrete subgroup of R 8 of full rank (i.e. it spans all of R 8).It can be given explicitly by the set of points Γ 8 ⊂ R 8 such that . all the coordinates are integers or all the coordinates are half-integers (a mixture of integers and half-integers is not allowed), and
The illegal firework explosion that took place in Aliamanu, Hawaii, also known as Salt Lake, has left five people dead and two arrested.
The designation E 7 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled A n, B n, C n, D n, and five exceptional cases labeled E 6, E 7, E 8, F 4, and G 2. The E 7 algebra is thus one of the five exceptional cases.