Q: What is the difference between irrational numbers and integers?

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They are all numbers

A rational number can be expressed as a ratio of two integers, p/q where q > 0. An irrational number cannot be expressed in such a way.

no

There are numbers which cannot be expressed as ratios of two integers. These are called irrational numbers.

No prime numbers are irrational: All prime numbers are integers, and all integers are rational, since they can be expressed as themselves divided by 1.

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Directed numbers have a positive or negative sign associated with them. (The positive sign may be implied). They can be rational fractions (including mixed numbers) or irrational. Integers cannot be fractions or irrational.

Integers are whole numbers, therefore they are not irrational

No. In fact, integers are never Irrational Numbers.

No. Irrational numbers cannot be integers.

They are all numbers

No. Irrational numbers can not be expressed as a ratio between two integers.

A rational number can be expressed as a ratio of two integers, p/q where q > 0. An irrational number cannot be expressed in such a way.

no

No integers are irrational numbers. An integer is a whole number, positive or negative. This means they have no decimals or fractions. An irrational number, however, is a number with fractions or decimals. Therefor, there are no integers that are irrational numbers.

No. Prime numbers are positive integers, and integers are not irrational.

Natural numbers = Whole numbers are a subset of integers (not intrgers!) which are a subset of rational numbers. Rational numbers and irrational number, together, comprise real numbers.

All natural numbers are rational numbers. No irrational numbers are natural numbers.