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Example:Prove the Number is Irrational

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Explanation:

In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q

The decimal expansion of a rational number always either terminates after finitely many digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. 

 

http://en.wikipedia.org/wiki/Rational_number

 

An irrational number is any real number which cannot be expressed as a fraction a/b, where a and b are integers, with b non-zero, and is therefore not a rational number. (Our solved example in mathguru.com uses this concept).

Informally, this means that an irrational number cannot be represented as a simple fraction. Irrational numbers are precisely those real numbers that cannot be represented as terminating or repeating decimals. The real numbers are uncountable .It follows that almost all real numbers are irrational. Irrational numbers include √2, π, and e.

 

http://en.wikipedia.org/wiki/Irrational_number

 

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.