Want knowledge tree and some concepts!

Want knowledge tree and some concepts!

Rationals include:
1) Natural number: number 0,1,2,3,... It's called a natural number.
2) Positive number: A number larger than 0 is called a positive number.
3) Negative number: the number with "—"(read "negative ") sign before positive number is called negative number. Negative numbers are less than 0.
4) Integer: positive integer,0 integer and negative integer are collectively referred to as integer.
5) Fractions: positive and negative fractions are collectively referred to as fractions.
6) Odd: An integer that is not a multiple of 2 is called odd. For example,-3,-1,1,5, etc. All odd numbers can be represented by 2n-1 or 2n+1, and n is an integer.
7) Even: An integer that is a multiple of 2 is called an even number. For example,-2,0,4,8, etc. All even numbers can be represented by 2n, and n is an integer.
8) Prime number: if an integer greater than 1 has no other factor except 1 and itself, this number is called prime number, or prime number, for example,2,3,11,13, etc.2 is the smallest prime number.
9) Total number: if an integer greater than 1 has other factors besides 1 and itself, this number is called total number, such as 4,6,9,15, etc.4 is the smallest total number.
10) Co-prime: If two positive integers have no other factors than 1, these two integers are called co-prime, such as 2 and 5,9 and 13.
A rational set is a field in which four operations can be performed (except for the division of 0), and for these operations, the following operation laws hold (a, b, c, etc. all represent arbitrary rational numbers):
1 Commutative law of addition a+b=b+a;
2 The combination of addition a+(b+c)=(a+b)+c;
3 The existence number 0, make 0+a=a+0=a;
4 For any rational number a, there exists an additive inverse, denoted by -a, such that a+(-a)=(-a)+a=0;
5 Commutative law of multiplication ab=ba;
6 The binding law of multiplication a (bc)=(ab) c;
7 Distributive law a (b+c)=ab+ac;
8 There is a multiplicative unit 1=0 such that for any rational number a,1a=a;
9 For a rational number a which is not 0, there is a multiplicative inverse 1/a such that a (1/a)=(1/a) a=1.
100 A =0 A number multiplied by 0 is also equal to 0.
Moreover, the rational number is an order field, that is, there is an order relation ≤ on it.
The absolute value of 0 is still 0.

Reciprocal. Rational. Inverse. What is the concept of absolute?

[Natural number ]1,2,3,4, etc. representing the number of objects are called natural numbers.
If an integer greater than 1 can not be divided by any positive integer other than itself and 1, then this number is called a prime. If a number greater than 1 can be divided by any positive integer other than itself and 1, then this number is a composite, and 1 is neither a prime nor a composite.
Only two real numbers with different signs, one of which is called the opposite number of the other.
Absolute value An absolute value of a positive number is itself, an absolute value of a negative number is its opposite, and an absolute value of zero is zero.
On the number axis, the absolute value of a real number is the distance from the origin of the number.
A quotient of a nonzero real number divided by one is the reciprocal of the real number. Zero has no reciprocal.
If the square of a rational number a is equal to the rational number b, then the rational number b is called the complete square.
If the nth power of a number (n is an integer greater than 1) equals a, the number is called the nth power of a.
The operation of finding the root of a number is called the square.
[Arithmetic root] The positive nth power root of the positive number a is called the nth power arithmetical root of a, the arithmetical root of zero is zero, and the negative number has no arithmetical root.
Algebraic Expression: An expression obtained by connecting letters of numbers or numbers with finite degree operation symbols (add, subtract, multiply, divide, multiply, and square).
The result of the calculation of a number in place of a letter in an algebraic expression is called the value of the algebraic expression when the letter takes the number.
[Classification of Algebras]
A rational expression is an algebraic expression that contains only addition, subtraction, multiplication, division, and power operations
An algebraic expression containing letters under the radical is called irrational
A rational expression without division or without a division but with no letter in it is called an integer.
A rational form containing letters in a division is called a fraction.