# How are rational and irrational numbers related?

Rational and irrational numbers are mutually exclusive but jointly or collectively exhaustive set of real numbers.

There is only one set of rational and irrational numbers. These two characteristics are crucial.

Irrational numbers in decimal notation have non-terminating non-repeating (or non-recurring decimals), whereas rational numbers terminate after the decimal sign or have non-terminating but repeating (or recurring decimals).

To put it briefly, a set of real numbers that is jointly or collectively exhaustive but mutually exclusive can be categorized as rational and irrational numbers.

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Rational and irrational numbers are both subsets of real numbers. Rational numbers can be expressed as the quotient of two integers, while irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions. Together, rational and irrational numbers make up the entire set of real numbers. Additionally, the sum, difference, product, and quotient of a rational number and an irrational number can result in an irrational number. However, the sum, difference, product, or quotient of two rational numbers is always a rational number.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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