Random sequences

Introduction

We consider the case of series of numbers which, in the strict sense of the definition, are actually not series of numbers. We throw a dice$\mathit{N}$-mal and write the $\mathit{N}$ Numbers as a "sequence of numbers":

$${\mathit{r}}_{\mathit{n}}=\underset{\underset{\mathit{N}\text{values}}{︸}}{2,5,6,1,3,4,\dots ,3}$$

Since the number of pips is not predictable when rolling the dice, so randomly one of the values $1,\dots ,6$ assumes, we denote ${\mathit{r}}_{\mathit{n}}$ as a random sequence. So it follows: ${\mathit{r}}_{\mathit{n}\mathrm{+1}}$ is not off ${\mathit{r}}_{\mathit{k}}$ with $\mathit{k}\le \mathit{n}$ derivable! In other words: for the sequence of numbers ${\mathit{r}}_{\mathit{n}}$ there is no education law. Hence is ${\mathit{r}}_{\mathit{n}}$ in the strict mathematical sense no sequence of numbers. Therefore it is common to refer to such sequences of random numbers as random sequences. This is permissible if we replace the term “education law” mentioned at the beginning with “education process”. In the case of the arithmetic sequence, the law of formation reads

$${\mathit{a}}_{\mathit{n}}={\mathit{a}}_{\mathit{n}-1}+\mathit{d}$$

the corresponding educational process is the “Take ${\mathit{a}}_{\mathit{n}-1}$ and add $\mathit{d}$, around ${\mathit{a}}_{\mathit{n}}$ to obtain. “In this sense then is also ${\mathit{r}}_{\mathit{n}}$ a sequence of numbers, because there is the formation process “Note the eye number of the $\mathit{n}$-Turn the die and set them equal ${\mathit{r}}_{\mathit{n}}$. “In general we say: a random process results in a random sequence. The cube is a special example of regular polyhedra, i.e. bodies that are bounded by congruent regular polygons and have congruent regular corners. The random process with e.g. a dodecahedron thus provides a random sequence of numbers $1,2,\dots ,11,12$.

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