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Q: Is an irrational number the same as whole numbers?

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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.

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.

No. An irrational number isn't a whole number, nor can it be represented exactly as a fraction of two whole numbers. 50 is a whole number, so it's rational. 50/3, while having a repeating decimal, is still rational because it's an exact fraction. The square root of two is irrational because there is no fraction that can exactly represent it. The same goes for pi (although 22/7 is close enough for government work -- jk).

There are very many uses for irrational numbers. A square, whose sides are a rational number, will have a diagonal of irrational length. The diagonals of most rectangles, with rational sides, will be irrational. The circumference and area of a circle (or ellipse) is related to pi, an irrational number. In the same way that pi is central to geometry, another irrational number, e, is fundamental to advanced calculus.

Whole numbers and natural numbers are the exact same, except that whole numbers include zero

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No. Perfect squares as the squares of the integers, whereas irrational squares as the squares of irrational numbers, but some irrational numbers squared are whole numbers, eg √2 (an irrational number) squared is a whole number.

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.

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.

Numbers cannot be rational and irrational at the same time.

The difference is that rational numbers stay with the same numbers. Like the decimal 1.247247247247... While an irrational number is continuous but does not keep the same numbers. Like the decimal 1.123456789...

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.

There are very many uses for them. A square, whose sides are a rational number, will have a diagonal of irrational length. The diagonals of most rectangles, with rational sides, will be irrational. The circumference and area of a circle (or ellipse) is related to pi, an irrational number. In the same way that pi is central to geometry, another irrational number, e, is fundamental to advanced calculus.

Each integer is a whole number and each whole number is an integer. So the set of all integers is the same as the set of all whole numbers. By the equivalence of sets, integers and whole numbers are the same.

Each integer is a whole number and each whole number is an integer. So the set of all integers is the same as the set of all whole numbers. By the equivalence of sets, integers and whole numbers are the same.

An irrational number is a number that can't be written as a fraction with whole numbers on top and bottom.An irrational number written as a decimal never ends. BUT, some rational numbersdo the same thing, so you can't say that just because the decimal never ends, itmust be an irrational number.Here are some rational numbers whose decimals never end:1/31/61/71/91/11

Both rational and irrational numbers can be expressed with decimals. If the number is irrational, it will have an infinite number of decimal digits, and there will be no periodic repetition. For example, 1/7 (which is rational) is 0.142857 142857 142857... The same sequence of six digits repeats over and over again. In irrational numbers, this is not the case.

Yes. The infinity of rational numbers has the same size as the natural numbers, said to be "countable". The infinity of real numbers (and therefore, also of irrational numbers) is a larger infinity, said to be "uncountable".

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