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calculated with any accuracy, but can’t be changed by a rational number.
They can appear as results of geometrical measurements, for example:
- a ratio of a square diagonal length to its side length is equal to
- a ratio of a circumference length to its diameter length is an irrational number
Examples of another irrational numbers: The Real Numbers
The real numbers are those representable by an infinite decimal expansion, which may be repeating or
nonrepeating; they are in a one-to-one correspondence with the points on a straight line and are sometimes
referred to as the continuum. Real numbers that have a nonrepeating decimal expansion are called irrational,
i.e., they cannot be represented by any ratio of integers. The Greeks knew of the existence of irrational numbers
through geometry; e.g., 2 is the length of the diagonal of a unit square. The proof that 2 is unable to be
represented by such a ratio was the first proof of the existence of irrational numbers, and it caused tremendous
upheaval in the mathematical thinking of that time. Imaginary and complex numbers
Consider the pure quadratic equation:
x2 = a ,
where a – a known value. Its solution may be presented as:
Math I - 18 - Feel free to pass this on to your friends, but please don’t post it online.
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- Spring '13
- Elementary arithmetic, college entrance exam