It is proved that the sum of a rational number and an irrational number must be an irrational number

If x+y=z, where x is a rational number and y is an irrational number, let x=a/b (a, b are integers).
Using the inverse method, if z is a rational number, then z can represent the form of the component number, i.e. z=c/d (c, d is an integer)
Y=z-x=c/d-a/b=(cb-ad)/bd, and (cd-ad)/bd is a fraction, which indicates that y is a rational number and contradicts the problem. Therefore, the assumption is not true, so z is an irrational number.

Are finite decimals rational? Are finite decimal numbers rational?

Yes!

RELATED INFORMATIONS

1. Is infinite cyclic decimal a rational number? What about infinite non-recurring decimals? Why?
2. Is the seventh of the negative rational number, irrational number is the fraction of rational number.
3. The absolute value of a rational number is non-negative, i.e.|a| equals what?
4. If the correct sum of two numbers is negative, then at least one of the two numbers is negative and the absolute value of the sum of two rational numbers is equal to the absolute value of the two numbers
5. The absolute value of a rational number is equal to the opposite number of the number,
6. Given that the quotient of two rational numbers is negative, then,
7. If the product of two rational numbers is positive and the sum of two rational numbers is negative, then both numbers A are positive and B are negative. If the product of two rational numbers is positive and the sum of two rational numbers is negative, then two rational numbers are A is a positive number, B is a negative number, C is a positive number, D has one zero If the product of two rational numbers is positive and the sum of two rational numbers is negative, then both numbers A are positive and B are negative. If the product of two rational numbers is positive and the sum of two rational numbers is negative, then two rational numbers are A is a positive number and B is a negative number. D has one zero
8. If the quotient of two rational numbers is positive, then the two numbers must be () A. All negative B. Both are positive C. At least one is positive D. Same number
9. If the quotient of two rational numbers is negative, then the two numbers are both positive A or negative B has at least one negative C and one positive D a negative If the quotient of two rational numbers is negative, then the two numbers are both positive A or negative B at least one of which is negative C and is positive D a positive number a negative number
10. For a rational number represented by the letter a, is it positive or negative
11. On Rational and Irrational Numbers Irrational number multiply irrational number; irrational number divide irrational number; irrational number add irrational number; irrational number subtract irrational number; rational number multiply irrational number; rational number divide irrational number; rational number add irrational number; rational number subtract irrational number
12. In the following numbers, the irrational number is () (A) Root 36(B) Root (-4)2(C)0.2020020002(D)8/3
13. Which two irrational numbers add up to five?
14. If the sum of two irrational numbers is 5, the two irrational numbers may be ______(fill in two specific numbers).
15. Write two irrational numbers with a sum of 5(two numbers are different)
16. Is it true that real numbers are either irrational or rational? Is it true that irrational numbers are infinite decimals?
17. An irrational number is a number that can not be opened by the square,
18. Is it right to say that "the number that can not be opened is irrational "? Is it right to say that the number that can not be opened is irrational?
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