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

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

... of rational numbers. Every rational number in \$\mathbb{R} ... Irrational and rational sequence ... of \$\Bbb R\$ means that there exists \$n ...
Positive: 56 %
... 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 ...
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+ ...
Positive: 56 %
... 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 ...
Positive: 51 %
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, ...