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Supremum-and-infimum
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Which of the following statements are true for $A=\{t\sin(\frac{1}{t})\ |\ t\in (0,\frac{2}{\pi})\}$?
December 1st, 2020
real-analysis
supremum-and-infimum
Question about supremum $\implies$ infimum
August 1st, 2022
order-theory
supremum-and-infimum
ordered-fields
real-analysis
Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$
August 1st, 2022
real-analysis
supremum-and-infimum
Does maximum or supremum of an infinite set exit?
August 1st, 2022
supremum-and-infimum
Find $\sup$ and $\inf$ of $(\frac{1}{n})$
October 29th, 2020
real-analysis
supremum-and-infimum
Interchanging limit and supremum
September 13th, 2020
limits
supremum-and-infimum
inequality
sequence-of-function
If $\sup S\not\in S$ then $\{x \in S: x > \sup{S} - \epsilon\}$ is infinite
September 12th, 2020
supremum-and-infimum
real-analysis
proof-writing
If sup A $\lt$ sup B show that an element of $B$ is an upper bound of $A$
August 1st, 2022
proof-verification
proof-writing
real-numbers
supremum-and-infimum
real-analysis
change the order of sup and inf
September 28th, 2020
examples-counterexamples
analysis
supremum-and-infimum
Is supremum part of the set or it is the bigest element out of it?
November 18th, 2020
analysis
supremum-and-infimum
real-numbers
proving if $a \le b$ then $\sup(A) \le \inf(B)$
October 11th, 2020
supremum-and-infimum
proof-verification
self-learning
Approximation Property for Infimum
August 1st, 2022
real-analysis
supremum-and-infimum
proof-verification
If a monotone sequence is convergent, does this imply boundedness?
August 1st, 2022
supremum-and-infimum
real-analysis
limits
convergence-divergence
very simple statement but how to find inf, sup
November 29th, 2020
real-analysis
supremum-and-infimum
proof-writing
Simple question about square of a supremum
December 24th, 2021
supremum-and-infimum
real-analysis
compact set always contains its supremum and infimum
April 23rd, 2020
real-analysis
analysis
supremum-and-infimum
compactness
Supremum Infimum argument: what did I do wrong?
August 1st, 2022
supremum-and-infimum
real-analysis
proof-verification
How can a finite set not have a maximum or minimum?
March 23rd, 2020
supremum-and-infimum
elementary-set-theory
real-analysis
Proving that $\inf A=\sup B$
August 1st, 2022
real-analysis
supremum-and-infimum
Prove the limit superior of a bounded sequence converges
August 1st, 2022
proof-verification
limits
sequences-and-series
real-analysis
supremum-and-infimum
Prove that the closure contains the supremum
August 1st, 2022
proof-writing
supremum-and-infimum
real-analysis
Let $A$ be bounded below, and $B = \{b \in R : b$ is a lower bound for $A\}$. Show that $\sup B = \inf A$.
July 16th, 2020
supremum-and-infimum
real-analysis
proof-verification
Find the infimum and supremum of $\{x\in Q \mid x² < 9\}$
October 26th, 2020
supremum-and-infimum
analysis
limits
calculus
Sup and inf of $n \sin(1/n)$
August 29th, 2021
supremum-and-infimum
analysis
Let $S=\{\frac{1}{n}-\frac{1}{m}:n,m\in \mathbb{N}\}$ Show that $\sup S = 1$
September 18th, 2020
real-analysis
supremum-and-infimum
Proving the nested interval theorem
August 6th, 2020
supremum-and-infimum
cauchy-sequences
self-learning
proof-writing
Prove that $\sup(S-T)=\sup S-\inf T$
August 1st, 2022
supremum-and-infimum
proof-verification
real-analysis
If $A$ is an ordered set has the Least upper bound property iff it has the greatest lower bound property.
August 1st, 2022
proof-verification
supremum-and-infimum
order-theory
Prove that $\sup(A)<\sup(B)$ implies there is an upper bound of $A$ in $B$
August 1st, 2022
real-analysis
supremum-and-infimum
Prove that $\sup{A} = \inf{B}$ if and only if for each $\delta > 0$ there exists $x \in A$ and $y \in B$ such that $x + \delta > y$:
August 19th, 2020
supremum-and-infimum
proof-verification
real-analysis
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