Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999 Association of Mizar Users

## Irrationality of $e$

Freek Wiedijk
University of Nijmegen
Written while a guest of the Institute of Mathematics of the University of Bia{\l}ystok.

### Summary.

We prove the irrationality of square roots of prime numbers and of the number $e$. In order to be able to prove the last, a proof is given that {\tt number\_e = exp(1)} as defined in the Mizar library, that is that $$\lim_{n\rightarrow\infty} (1+{1\over n})^n = \sum_{k=0}^\infty {1\over k!}$$

#### MML Identifier: IRRAT_1

The terminology and notation used in this paper have been introduced in the following articles [21] [2] [18] [20] [1] [13] [4] [11] [9] [16] [15] [10] [3] [6] [17] [5] [12] [22] [8] [19] [7] [14]

#### Contents (PDF format)

1. Square Roots of Primes are Irrational
2. A proof that $e = e$
3. The Number $e$ is Irrational

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