We first want to remind the reader of the different kinds of numbers, that are used in arithmetics and to visualize their relationships with the elementary arithmetic operations. Here the number is the operand on which a certain operation is applied (arithmetic operations such as +,-,*,/,,,,, logical operations such as and, or, not, if-then, otherwise, ...).
The definitions of the numbers and arithmetic operations are up to the complex numbers synchronized in such a way. that for all number the following fundamental rules of arithmetic operations apply. here means, that the operation in brackets is executed first.
The requirement to apply certain operations, that had been introduced for a certain kind of number, without restrictions lead to successive extensions of the usual concepts of numbers.