A non-negative integer set is a specific set, which refers to the set of all natural numbers, and is often represented by the symbol n. A non-negative integer includes positive integers and zeros, and is a countable set. The set of all nonnegative integers is usually called the set of nonnegative integers (or natural number set). Non-negative integer sets include natural numbers such as 0, 1, 2 and 3. Mathematically, the set of non-negative integers is represented by the bold capital letter n.

Non-negative integers include positive integers and zeros. A set of nonnegative integers is a countable set. The potential of non-negative integer set is strictly smaller than that of real number set, that is, there is no one-to-one correspondence between them (see diagonal argument for details). In fact, the potential of real number set is 2N0, which is the potential of natural number set's power set. Natural number, nonnegative/positive integer (1, 2, 3, 4 ...).

One reason for thinking that natural numbers do not contain zero is that people start learning numbers with "one, two, three" instead of "zero, one, two, three …", because it is unnatural.

Non-negative integer:

Natural numbers usually have two functions: they can be used for counting, see radix; Can also be used for sorting, see ordinal number. The set of natural numbers is a countable infinite set with no upper limit. Mathematicians generally use n to represent it. (N* represents a natural number other than 0) There are addition and multiplication operations on the set of natural numbers, and the result of addition or multiplication of two natural numbers is still a natural number.

You can also do subtraction or division, but the result of subtraction and division is not necessarily a natural number, so subtraction and division operations may not be established in the set of natural numbers. Natural number is the most basic digital system known to people.

In order to make the number system have a strict logical basis, mathematicians in the19th century established two theories about natural numbers: ordinal number theory and cardinal number theory, which made the concept, operation and related properties of natural numbers strictly discussed. The addition and multiplication of natural numbers can be defined by ordinal number or cardinal number theory, and the operations under the two theories are consistent.