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rational number
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rational number

In mathematics, any number that can be expressed as an exact fraction (with a denominator not equal to 0), that is, as a ÷ b where a and b are integers; or an exact decimal. For example, 2/1, 1/4, 15/4, −3/5 are all rational numbers, whereas π (which represents the constant 3.141592 ... ) is not. Numbers such as π are called irrational numbers.



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The rationals is this: Pass/fail thresholds are much easier and clearer to meet, defend, and communicate.
4 as P(t) := {(c, d), c, d [greater than or equal to] 1, ct [less than or equal to] 1, dt [less than or equal to] 1, (c + d)t > 1, (c, d) = 1}, and, for a pair (a/c, b/d) of rationals satisfying ad - bc = -1, denote by S(a/c, b/d) the intersection of B \ F with the vertical strip {(a/c) [less than or equal to] x [less than or equal to] (b/d)}.
Aleph-one counts all the real numbers--the rationals plus the irrationals such as pi and the square root of z.
 
 
 
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