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Book: MathDiscovery

See: Math, 20110402 Math Deep Structure, 20160620 Discovery in Mathematics

Discovery in Mathematics: A System of Deep Structure

How does the three-cycle extend our existing mathematical language?

Zermelo-Fraenkel axioms of set theory


Implicit math: Sets are simplexes. Are simplexes defined by their subsimplexes as well?

Eightfold way


Relate to multiplication


Total order is the same as a labeled simplex.

Extension: 3! + (4 + 4 + 4 + 6) = 4!

3! = 2! + 4 (representations: 2 for edge and 4 for vertex)

We may assign the weight q^(k-1) to the kth vertex and the weights 1/q to each new edge. These weights give each vertex a unique label. The weight of each k-simplex is then the products of the weights of their vertices and edges. The Gaussian binomial coefficients count these weighted k-simplexes. Without the weights the vertices are distinct but there is no way to distinguish them. The symmetry group is the Symmetric group which relabels the vertices.

Matematikos išsiaiškinimo būdai

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Puslapis paskutinį kartą pakeistas 2018 lapkričio 11 d., 16:39