The concept of natural number

The concept of natural number

Natural number
According to the current primary school textbooks, it is an integer greater than or equal to zero. It is used to measure the number of things or to indicate the order of things Natural numbers start from 1, one after another, and form an infinite set. Natural number sets have addition and multiplication operations. The results of addition or multiplication of two natural numbers are still natural numbers, and they can also be used for subtraction or division, but the results of subtraction and division are not necessarily natural numbers, Therefore, subtraction and division are not always true in the set of natural numbers. Natural numbers are the most basic of all the numbers that people know. In order to make the system of numbers have a strict logical basis, mathematicians in the 19th century established two equivalent theories of natural numbers: ordinal number theory and cardinal number theory, which made the concept, operation and related properties of natural numbers strictly discussed
The theory of ordinal number was put forward by G. piano, an Italian mathematician. He summarized the properties of natural number and gave the following definition of natural number by axiom
The set of natural numbers n is a set that satisfies the following conditions: 1) there is an element in N, denoted as 1. 2) every element in n can find an element in n as its successor. 3) 1 is not the successor of any element. 4) different elements have different successors. 5) if any subset m of n is 1 ∈ m, and as long as X is in M, we can deduce that the successor of X is also in M, then M = n
Cardinal number theory defines natural number as the cardinal number of finite set. This theory proposes that two finite sets which can establish one-to-one correspondence between elements have the same quantitative characteristic, which is called cardinal number. In this way, all single element sets {x}, {y}, {a}, {B} have the same cardinal number, which is recorded as 1, They have the same cardinality, denoted as 2, etc. the addition and multiplication operations of natural numbers can be defined in ordinal number theory or cardinality theory, and the operations under the two theories are consistent

There is an operation program, which can make: a ♁ B = n (n is a constant)
（a+1）♁b=n+1,a♁（b+1）=-2,
Now we know that 1 ♁ 1 = 2, then, 2008 ♁ 2008 =?
The answer is - 2005

1♁1=2
2♁1=2+1
2♁2=2+1-2
♁ add one to each side, and the result will be minus one
So 2008 ♁ 2008 = 2-2007 = - 2005

If a ♁ B = n (n is a constant), we can get (a + 1) ♁ B = n + 1, a ♁ (B + 1) = n-2,
So 2013 ♁ 2013 =? Brothers and sisters,

1♁1=2 2♁1=2+1=3 1♁2=2-2=0
2♁1=3
3♁1=3+1=4
4♁1=4+1=5
…………
2003♁1=2004
2003♁2=2004-2=2002
2003♁3=2002-2=2000
2003♁4=2000-2=1998
…………
2003♁2003=-2000