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transcendental number |
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transcendental number: see number number, entity describing the magnitude or position of a mathematical object or extensions of these concepts.
The Natural NumbersCardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of ..... Click the link for more information. . transcendental numberNumber that is not algebraic, in the sense that it is not the solution of an algebraic equation with rational-number coefficients. The numbers e and π, as well as any algebraic number raised to the power of an irrational number, are transcendental numbers. |
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In 1882, mathematicians proved that pi is what they call a transcendental number, effectively ruling out the possibility of constructing a square out of a circle using only ruler and compass. They can be chosen, for example, by some complicated process of picking digits out of a very long, many-digit number, perhaps the product of a complicated sequence of squarings or factorings, or maybe a transcendental number -- pi, for example, calculated to hundreds of significant figures. |
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transcendental number
