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Every irrational number is NOT a rational number. For example, sqrt(2) is irrational but not rational.

A natural number is a counting number or a whole number, such as 1, 2, 3, etc. A rational number is one that can be expressed as a ratio of two whole numbers, which may be positive or negative. So, -2 is a rational number but not a counting number (it is an integer, though). Also, 2/3 is a rational number but not a whole, counting number or a natural number.

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Q: Why every irrational number is also a rational number but not every rational number is a natural number?

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No because they are rational numbers

No. Every real number is not a natural number. Real numbers are a collection of rational and irrational numbers.

Any, and every, irrational number will do.

When a rational numbers is divided by an irrational number, the answer is irrational for every non-zero rational number.

There is no such thing as a number that is both rational and irrational. By definition, every number is either rational or irrational.

Integers are rational. In the set of real numbers, every number is either rational or irrational; a number can't be both or neither.

Every whole number is rational.

No. No natural number can be irrational.

Such numbers cannot be ordered in the manner suggested by the question because: For every whole number there are integers, rational numbers, natural numbers, irrational numbers and real numbers that are bigger. For every integer there are whole numbers, rational numbers, natural numbers, irrational numbers and real numbers that are bigger. For every rational number there are whole numbers, integers, natural numbers, irrational numbers and real numbers that are bigger. For every natural number there are whole numbers, integers, rational numbers, irrational numbers and real numbers that are bigger. For every irrational number there are whole numbers, integers, rational numbers, natural numbers and real numbers that are bigger. For every real number there are whole numbers, integers, rational numbers, natural numbers and irrational numbers that are bigger. Each of these kinds of numbers form an infinite sets but the size of the sets is not the same. Georg Cantor showed that the cardinality of whole numbers, integers, rational numbers and natural number is the same order of infinity: aleph-null. The cardinality of irrational numbers and real number is a bigger order of infinity: aleph-one.

Every time. No exceptions.

No irrational number can turn into a rational number by itself: you have to do something to it. If you multiply any irrational number by 0, the answer is 0, which is rational. So, given the correct procedure, every irrational number can be turned into a rational number.

No, a real number could also be a rational number, an integer, a whole number, or a natural number. Irrational numbers fall into the same category of real numbers, but every real number is not an irrational number.

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