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| − | Real numbers can be thought of as numbers which can be represented by some finite or infinite decimal representation. | + | #REDIRECT [[Real number]] |
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| − | In classical physics, measurements of things that can vary smoothly and continuously, like speed or temperature, are treated as real numbers.
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| − | In a number line representation, the real numbers correspond to all the points on a geometric line. The distance between any two points on a line is a real number.
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| − | The real numbers include within them all of these other kinds of numbers:
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| − | *The "natural numbers" or positive integers, 1, 2, 3, ...
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| − | *Zero and the negative integers
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| − | *Fractions, like 355/113
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| − | *Any decimal representation which terminates (comes to an end), like 6.023, because this is just a way of writing a fraction (in this case, 6023/1000)
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| − | *Any decimal representation which repeats or recurs, like 1.86292929292929..., because these can be shown to be fractions
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| − | *Irrational numbers, like &sqrt;10 = 3.162277660168... π = 3.1415926525..., whose decimal representations never repeat or terminate.
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| − | Formally, real numbers are defined as the unique [[Field (mathematics)|field]] which is [[Ordered]], [[Complete (mathematics)|Complete]], and [[Archimedean]]. The reals can be constructed from the rationals by means of [[Dedekind cuts]] or [[Cauchy Sequences]].
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| − | ==Notes and references==
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| − | <references/>
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