a sequence {xn} of real numbers is contractive if ∃ a constant C > 0, 0 < C < 1, such that |xn+1 − xn| ≤ C|xn − xn−1| for all n ∈ N.
54427
$\left|x_{n+1} - x_n\right| < C\left|x_n - x_{n-1}\right|$ prove this is Cauchy
98167
If a sequence $(u_n)$ be such that its every subsequence has a subsequence that converges to $0$, then $\lim u_n= 0$
129393
Product of bounded and convergent to $0$ sequence is a convergent to $0$ sequence
63608
Cauchy sequence in a normed space
118328
Metric space is totally bounded iff every sequence has Cauchy subsequence
154578
Proving there is a sequence convergent to a limit point of a set without axiom of countable choice?
99117
Existence of a sequence of positive continuous functions on $\mathbb R$ which is unbounded precisely on $\mathbb Q$
8814
Proving that a sequence such that $|a_{n+1} - a_n| \le 2^{-n}$ is Cauchy
9789
Convergence of a sequence of non-negative real numbers $x_n$ given that $x_{n+1} \leq x_n + 1/n^2$.
60024
Proof that a sequence is convergent
45885
If there exist sequence such that $g(x_n)=f(x_{n+1})$, then we have $g(x_0)=f(x_0)$ for some $x_0$
124380
existence of sequence of polynomial
98634
What is a counterexample for If $x\in\overline{A},$ $x$ is not necessarily a limit of a sequence in $A$?
1396
cardinality of all real sequences
46323
Criteria for convergent sequence (Baby Rudin Theorem 3.22)
78472
Sequence is periodic $x_{n+2}=|x_{n+1}-x_{n-1}|$
63523
$|a_{n+1}-a_n| \leq \frac{1}{2} |a_{n}-a_{n-1}|$. Prove $(a_n)$ is Cauchy