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Why does the sum of rational number and irrational numbers are always irrational?
Wiki User
∙ 10y ago
Let your sum be a + b = c, where "a" is irrational, "b" is rational, and "c" may be either (that's what we want to find out). In this case, c - b = a. If we assume that c is rational, you would have: a rational number minus a rational number is an irrational number, which can't be true (both addition and subtraction are closed in the set of rational numbers). Therefore, we have a contradiction with the assumption that "c" (the sum in the original equation) is rational.
Wiki User
∙ 10y ago
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The sum of rational numbers and an irrational number?
It is always an irrational number.
Is a real number always irrational?
Real numbers can be rational or irrational because they both form the number line.
What is an irrational plus two rational numbers?
Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.
Is the product of two rational numbers irrational?
The product of two rational numbers is always a rational number.
Are rational numbers is an irrational numbers?
yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.
The sum of rational numbers and an irrational number?
It is always an irrational number.
Is real number is always a rational number?
They are not. Sometimes they are irrational. Irrational numbers cannot be expressed as a fraction.
Is a real number always irrational?
Real numbers can be rational or irrational because they both form the number line.
What is an irrational plus two rational numbers?
Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.
Is the product of two rational numbers irrational?
The product of two rational numbers is always a rational number.
Can irrational numbers be rational numbers?
No. If it was a rational number, then it wouldn't be an irrational number.
Is 1210 a irrational number?
Whole numbers are always rational.
Are rational numbers is an irrational numbers?
yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.
Are some rational numbers are irrational numbers?
Numbers cannot be rational and irrational at the same time.
Is the product of a rational number and irrational number always rational?
No.A rational times an irrational is never rational. It is always irrational.
The rational numbers are a subset of the irrational numbers?
No, they are complementary sets. No rational number is irrational and no irrational number is rational.Irrational means not rational.
List of rational and irrational numbers?
-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.
