What Is A Finite Set Of Rational Numbers

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What Is A Finite Set Of Rational Numbers

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Chapter 3 Finite State Automata 3 1 Deterministic Finite Automata

Rational numbers are one of the most commonly used numbers in the study of mathematics A rational number is defined as a number that can be put in the form eq frac a b eq where It is worth noting that any decimal expansion with a finite number of digits or a repeating expansion is rational. We can represent numbers like this using a line over the repeating digits, so 0 . 7 ̇ 1 ̇ 2 = 0 . 7 1 2 1 2 1 2. and 0 . 7 ̇ 1 ̇ 2 ∈ ℚ .

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What Is A Finite Set Of Rational NumbersWhy is the set of Rational numbers , Q Q, a countably finite set? I think that - if we assign n n to a rational number, and n + 1 n + 1 to another rational number, Then I can surely find a rational number in between these two, which is not accounted for. 1 Let q q be an irrational number and fix a positive integer N N Consider a small finite interval a b a b around q q Let U U be the set of rational numbers of the form m n m n such that gcd m n 1 g c d m n 1 n N n N and a m n b a m n b Show that U U is finite

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