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yes they do. because a rational number is any number that can be made into a fraction there is no field axiom which goes against this. For example the multiplicative identity. 5/6 times 1 equals 5/6 exc....

Q: Do all rational numbers apply to the 11 Field axioms?

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Yes, it applies to even multiplication of fractions and rational and irrational numbers.

The set of rational number satisfies the following properties with regard to addition: for any three rational numbers x, y and z, · x + y is a rational number (closure under addition) · (x + y) + z = x + (y + z) (associative property of addition) · There is a rational number, 0, such that x + 0 = 0 + x = x (existence of additive identity) · There is a rational number, -x, such that x + (-x) = (-x) + x = 0 (existence of additive inverse) · x + y = y + x (Abelian or commutative property of addition)

As soon as you introduce fractions (even division by 1), the concept of "next" can no longer apply. There are infinitely many rational numbers between any two numbers. So between any number an a potential "next" number, there are infinitely many numbers.

The set of integers is closed under addition so that if x and y are integers, then x + y is an integer.Addition of integers is commutative, that is x + y = y + xAddition of integers is associative, that is (x + y) + z = x + (y + z) and so, without ambiguity, either can be written as x + y + z.The same three rules apply to addition of rational numbers.

That could apply to numbers from 5500 to 6499.

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Postulates and axioms.

Yes, a rational number is a real number. A rational number is a number that can be written as the quotient of two integers, a/b, where b does not equal 0. Integers are real numbers. The quotient of two real numbers is always a real number. The terms "rational" and "irrational" apply to the real numbers. There is no corresponding concept for any other types of numbers.

Yes, it applies to even multiplication of fractions and rational and irrational numbers.

Operations on rational numbers refer to the mathematical operations carrying out on two or more rational numbers. A rational number is a number that is of the form p/q, where: p and q are integers, q ≠ 0. Some examples of rational numbers are: 1/2, −3/4, 0.3 (or) 3/10, −0.7 (or) −7/10, etc. We know about fractions and how different operators can be used on different fractions. All the rules and principles that apply to fractions can also be applied to rational numbers. The one thing that we need to remember is that rational numbers also include negatives. So, while 1/5 is a rational number, it is true that −1/5 is also a rational number. There are four basic arithmetic operations with rational numbers: addition, subtraction, multiplication, and division.

The concepts "even" and "odd" apply to whole numbers. They don't make sense for other classes of numbers, such as rational numbers, real numbers, complex numbers, etc.

No they cant because that would be contradicting each other ( The numbers wont end and don't have a pattern but rational is the complete opposite)

0 and 1 (and -1) are the only integers which are not prime nor composite. All non-integral numbers are also non-prime and non-composite. This is because the property is not defined for such numbers.

Rational numbers are numbers that can be expressed as a fraction of two integers. For example, 2/3, 8/27, and 4/1 are all rational numbers. In decimal form, those three numbers would be written as .66666666666... (I'm using the "..." to represent the fact that those 6's after the decimal point continue on forever), .296296296296296..., and 4, respectively. Notice how those three numbers, when written in decimal form, either repeat some pattern after their decimal point, or end. This is, in fact, the case for every rational number; they either terminate, or they have an infinite amount of some repeating number or group of numbers after their decimal point.Irrational numbers differ from rational numbers in that none of the above apply; i.e., they can't be expressed as a fraction of two integers, they don't repeat indefinitely, and they don't end. A couple of famous examples of irrational numbers are pi and the square root of two.

The set of rational number satisfies the following properties with regard to addition: for any three rational numbers x, y and z, · x + y is a rational number (closure under addition) · (x + y) + z = x + (y + z) (associative property of addition) · There is a rational number, 0, such that x + 0 = 0 + x = x (existence of additive identity) · There is a rational number, -x, such that x + (-x) = (-x) + x = 0 (existence of additive inverse) · x + y = y + x (Abelian or commutative property of addition)

As soon as you introduce fractions (even division by 1), the concept of "next" can no longer apply. There are infinitely many rational numbers between any two numbers. So between any number an a potential "next" number, there are infinitely many numbers.

all three apply

Once you familiarize yourself with the basic axioms and theorems of geometry, you will be able to see how they apply to the proof of any particular problem that you may be working on.