From Derangement To Euler’s Number | Mathematics - Medium

How e can rise from combinatorics by Eliran Turgeman in Cantor’s Paradise.

From Derangement To Euler’s Number

The constant e has a significant role across mathematics from growth problems to compound interest and even eigenvalues problems.

e has many representations, some of the most well known are

some of many e representations

If the above formulation seems unfamiliar or daunting to you, don’t get discouraged since it’s not gonna be relevant for this article. In this article, I will discuss a totally different approach to how we can get an approximation of e solving a simple and intuitive combinatorics problem...

Say a postman has n letters and every one of these letters is addressed to a different person. Assuming that our postman is a bit clumsy and he delivers the letters randomly, what are the chances for derangement? or in other words, what are the chances that no one will get a letter which is addressed to them?...

Conclusion

Starting off with an intuitive combinatorial problem that seems completely unrelated to e, we managed to give rise to one of the most significant constants in mathematics.

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Source: Medium