Binomial coefficients are the numbers that appear in the Binomial theorem, and also in Pasal's triangle. They are also naturally related to paths in Pascal's array, essentially the difference table associated to the triangular numbers. We also relate binomial coefficients to the rising and falling powers notation introduced by Knuth.This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. The full playlist is at http://www.youtube.com/playlist?list=PL5A714C94D40392AB&feature=view_all
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