Show that every real number is a limit of rational number.
124448
For every real number $a$ there exists a sequence $r_n$ of rational numbers such that $r_n$ approaches $a$.
121831
Proving that rational numbers are dense
140817
Real Analysis Inequality Proof Involving Reals and Rationals $0 < |r - q| < \varepsilon$
106960
Proof to sequences in real analysis
152126
Suppose every subsequence of X converges to 0. Show that lim(X)=0
143227
Show that: $\lim \limits_{n\to\infty}\frac{x_n-x_{n-1}}{n}=0 $
98755
How can I show that the set of rational numbers with denominator a power of two form a dense subset of the reals?
39621
Let a, b, c, d be rational numbers...
153969
The "elements" of a real number
31744
Proving that there is an irrational number between any two unequal rational numbers.
86893
Show that it is impossible to list the rational numbers in increasing order
34710
Cardinality of Irrational Numbers
9966
Range of a Rational Function
41767
Sequence of rational numbers converging to an arbitrary irrational number $\beta$.
32848
Prove that the product of a non-zero rational and irrational number is irrational.
33310
Proving that the set of limit points of a set is closed
23752
Proving Irrationality