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irrational number
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irrational number

Number that cannot be expressed as an exact fraction. Irrational numbers include some square roots (for example, √2, √3, and √5 are irrational); numbers such as π (for circles), which is approximately equal to the decimal 3.14159; and e (the base of natural logarithms, approximately 2.71828). If an irrational number is expressed as a decimal it would go on for ever without repeating. An irrational number multiplied by itself gives a rational number.
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It is hard to introduce (or review) fractions, and present convincing examples of numbers that are not fractions, namely, irrationals.
Conceptual complexity and apparent contradictions in mathematics ... by Gough, John / Australian Mathematics Teacher
Aleph-one counts all the real numbers--the rationals plus the irrationals such as pi and the square root of z.
Hotel Infinity by Gardner, Martin / New Criterion
Given the fact that the interval between 1 and the square root of 2 is less than 1/2, it might seem unfathomable that the numbers in this interval contain an uncountably infinite set of irrationals.
Mississippi Academy of Sciences: sixty-ninth Annual Meeting--February ... by Journal of the Mississippi Academy of Sciences
 
 
 
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