How do you prove that given any real number r there exists a sequence of rational numbers converging to r?

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... of rational numbers. Every rational number in $\mathbb{R} ... Irrational and rational sequence ... of $\Bbb R$ means that there exists $n ...
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... to all given elements of any subset of real numbers? ... than any number in $Z$. However, how do I prove ... {R}$, there is a rational sequence ...
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Positive: 53 %

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Math 171 Notes Prepared by Stefan ... for any real numbers r ≠ 1 and a, ... For each x é R, there exists an element -x é R such that x+ ...
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... Recall again that any real number is the limit of a sequence of rational numbers; pick x ∈ R, ... prove that there exists a real number ... you able ...
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a sequence given by a(n+1) = SQRT(2 + an) prove that it is converging.. ... prove that it is converging.. ... Thus for all real numbers x, ...
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Positive: 37 %

Some properties of Cauchy sequences. Any Cauchy sequence ... The fact that in R Cauchy sequences ... (a n) be a sequence of rational numbers converging ...
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Definition A sequence of real numbers is any function a : N→R. ... If there exists a sequence of closed ... separates the real numbers from the rational ...
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Axioms for the Real numbers. ... Equivalently: Given any x ∈ R, ... Between any two real numbers is an rational number. Proof
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How do I prove that between any two rational numbers there exists ... Number Theory: How do you prove ... number between any two given (positive) real ...
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If . are any two real numbers then there is a rational number ... showing Q' = R,IF YOU wish to do so ... Given any real x ,then for any ε>0 there exist a ...
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THE LIMIT OF A SEQUENCE OF NUMBERS DEFINITION OF THE NUMBER e: ... every real number M;there exists a natural ... the same as for a sequence of real numbers.
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A sequence of real numbers is a function f: N R. ... given any > 0, there exists at least one integer ... Prove that this sequence converges for any number b.
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... careful explanation of what the "real numbers ... and r(t) are given rational functions in the variable t. Then there exists some real number t 0 ...
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How do I find the counterexample to show that there is ... two any real number and rational ... any two rational numbers there exists at ...
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108 11 Rational and Irrational Numbers 11.1 Rational ... Then there exists a rational number r ... Between any two real numbers lies a rational number
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Rational and Real Numbers ... • Between any two rational numbers r and s there is another ... b ∈ R with a < b, there exists a rational number m/n ...
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56 %