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An irrational number is one that can not be written as a/b where a and b are integers

(whole numbers such as 5, -2, and 831).

Mathematically: A quantity which can not be expressed as the ratio of two integers.

Real numbers are any number you can find in the real world. For example:

-the square root of 2

-the length of a line (any line)

-pi (3.1415..........)

-The number of people in a flight

-The time it takes the water to boil

A more formal definition would be: Any number which does not have an imaginary component.

Q: What is the Definition of irrational numbers and real numbers?

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There are rational numbers and irrational numbers. Real numbers are DEFINED as the union of the set of all rational numbers and the set of all irrational numbers. Consequently, all rationals, by definition, must be real numbers.

The Real numbers

Pi is irrational. Irrational numbers, by definition, have no factors.

By definition, the two sets do not overlap. This is because the irrationals are defined as the set of real numbers that are not members of the rationals.

Some are and some aren't. 62 is real and rational. 1/3 is real and rational. sqrt(2) is real and irrational. (pi) is real and irrational.

Related questions

No. Irrational numbers by definition fall into the category of Real Numbers.

The set of real numbers is defined as the union of all rational and irrational numbers. Thus, the irrational numbers are a subset of the real numbers. Therefore, BY DEFINITION, every irrational number is a real number.

All irrational numbers are Real numbers - it's part of the definition of an irrational number. Imaginary numbers are neither rational nor irrational. An example of a number that is both Real and irrational is the square root of two. Another example is the number pi.

There are rational numbers and irrational numbers. Real numbers are DEFINED as the union of the set of all rational numbers and the set of all irrational numbers. Consequently, all rationals, by definition, must be real numbers.

A real number that can not be expressed as a rational number.

No, but the majority of real numbers are irrational. The set of real numbers is made up from the disjoint subsets of rational numbers and irrational numbers.

False. Irrational numbers are real numbers.

Irrational numbers are real numbers.

the collection of rational and irrational numbeers is known as real numbers

No. All irrational numbers are real, not all real numbers are irrational.

Irrational numbers are real numbers.

Real numbers are defined as the set of rational numbers together with irrational numbers. So rationals are a subset of reals, by definition.