Numbers on Aurélien's Math Notebook

Infinite Number of Primes

Sat, 22 Jul 2017 00:00:00 +0000

The erroneous proof I hear most often is: Suppose $P$ is a finite set that contains all the primes, then $p^* = 1 + \prod_{p \in P} p$ is prime. Indeed, the flaw is that $p^*$ is not necessarily prime but rather must be a multiple of some prime not in $P$.

Symbols

Sun, 08 Nov 2015 00:00:00 +0000

$$ \mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C} $$

Fibonacci numbers

Mon, 29 Jun 2015 00:00:00 +0000

The Fibonacci numbers are defined as $f_0 = 0,\ f_1 = 1$ and, for $i \ge 2,\ f_i = f_{i-1} + f_{i-2}$. Here is the beginning of the Fibonacci sequence:

$0, 1, 1, 2, 3, 5, 8, 13, 21, \ldots$

We generalize the definition above by changing the two initial values, for example with $f_0 = 4,\ f_1 = 6$ we obtain

$4, 6, 10, 16, 26, 42, \ldots$

Complex numbers division

Tue, 23 Jun 2015 00:00:00 +0000

$$ \frac{a+bi}{c+di} = \ldots $$