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I feel like talking about some pure math, just for fun on a Sunday afternooon. Back in 2006, Dan Christensen did something rather simple and got a surprisingly complex and interesting result. He took a whole bunch of polynomials with integer coefficients and drew their roots as points on the complex plane.
Contents 1. Why 0..1 Range While making demos I've found different interpolation tricks to be extremely valuable.
A set V consists of n elements if its elements can be counted 1, 2,..., n . In other words, the set V can be brought into a 1-1 correspondence with the set Often it's more convenient to start counting from 0. Then we get the set Definition A permutation is a 1-1 correspondence of a set V onto itself:
Let’s use the basic counting principle : There are 6 stages or events: digit 1, digit 2, digit 3, digit 4, letter 1, and letter 2. In general there are 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The first digit is limited to being the number 5, so there is only one possibility for that one. There are no restriction on digits 2 - 4, so each one of those has 10 possibilities. In general, there are 26 letters in the alphabet.
The factorial symbol is the exclamation point: ! So if I wanted to write 7 factorial it would be written as 7!. In general, n!