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Digital mathematics
Relationship among number, radix and bit weight: There are three elements in the carry counting system: number, radix and bit weight. Numbers refer to the position of a number in a number; Cardinality refers to the number of digits that can be used for each digit in a carry counting system.

For example, the radix of a binary number is 2, and the number of digits that can be used in each digit is 0 and 1. There is a rule in the number system. If it is an n-ary number, it must be 1 on every n-ary number. For multi-digits, the numerical value represented by "1" on a certain digit is called bit weight. For example, the bit weight of the second bit is 2 and the bit weight of the third bit is 4.

App application

In informal usage, cardinality is what is usually called counting. They are equal to natural numbers starting from 0 (i.e. 0, 1, 2). The most important thing is what can be formally defined as a finite cardinality. Infinite cardinality exists only in advanced mathematics and logic.

More formally, nonzero numbers have two purposes: to describe the size of a set or to describe the position of an element in a sequence. For finite sets and sequences, it is easy to see that these two concepts are consistent, because for all numbers describing a position in a sequence.