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Supremum-and-infimum
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Given $A, B \subset R$, both non-empty, show that $\inf{(A \cup B)} = \min{\{\inf{A}, \inf{B}\}}$
September 24th, 2020
proof-verification
supremum-and-infimum
real-analysis
Supremum/Infimum proof: $\sup \{1/x; x\in A\} = 1/\inf(A)$
August 1st, 2022
real-analysis
supremum-and-infimum
Why do we use supremum instead of maximum in Riemann Integration?
August 1st, 2022
supremum-and-infimum
calculus
riemann-integration
Supremum and infimum of $\{\frac{1}{n}-\frac{1}{m}:m, n \in \mathbb{N}\}$
August 1st, 2022
solution-verification
algebra-precalculus
supremum-and-infimum
Infimum of the Ky Fan metric achieved
September 12th, 2020
convergence-divergence
supremum-and-infimum
measure-theory
probability-theory
real-analysis
let $A_1, A_2, A_3, \dots$ be a collection of nonempty sets, each of which is bounded above. $(a)$ Find a formula for $\sup(A_1\cup A_2)$.
September 7th, 2020
real-analysis
supremum-and-infimum
The supremum of rationals that are less than a given number is equal to that number
August 1st, 2022
rational-numbers
supremum-and-infimum
real-analysis
Show that sup$AB$=(sup$A$)(sup$B$)
August 1st, 2022
proof-verification
proof-writing
supremum-and-infimum
real-analysis
Pointwise infimum of an arbitrary collection of upper semicontinuous functions is upper semicontinuous
October 10th, 2020
supremum-and-infimum
general-topology
real-analysis
semicontinuous-functions
Show $\sup{A}-\inf{B}=\sup\{a-b:a\in A, b\in B\}$
August 1st, 2022
supremum-and-infimum
real-analysis
Prove that $\sup(A-B) = \sup(A) - \inf(B)$
August 1st, 2022
supremum-and-infimum
Given that $x,y,z$ are positive reals such that $xyz=32$.What is the minimum value of $x^2+4xy+4y^2+2z^2$.
October 8th, 2020
supremum-and-infimum
calculus
Supremum of a sequence of functions
May 9th, 2020
real-analysis
supremum-and-infimum
What does Infimum of Upper Sum and Supremum of Lower Sums mean?
August 1st, 2022
integration
definite-integrals
supremum-and-infimum
riemann-integration
calculus
supremum and infimum example
August 1st, 2022
supremum-and-infimum
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
December 14th, 2020
real-analysis
supremum-and-infimum
solution-verification
Proof of $\sup AB=\max\{\sup A\sup B,\sup A\inf B,\inf A\sup B,\inf A\inf B\}$
August 1st, 2022
proof-verification
analysis
supremum-and-infimum
Is there a meaning to the notation "\arg \sup"?
July 19th, 2020
notation
supremum-and-infimum
definition
real-analysis
Finding the norm of the shift operator on $l^\infty$, $(x_1,x_2, \dots)\mapsto (x_2,x_3,\dots)$
August 1st, 2022
functional-analysis
supremum-and-infimum
lp-spaces
normed-spaces
linear-transformations
How to prove $\inf(S)=-\sup(-S)$?
August 4th, 2020
real-analysis
supremum-and-infimum
How can I show a supremum of a set is also its limit point?
August 1st, 2022
real-analysis
supremum-and-infimum
general-topology
What does the notation inf{...} mean?
August 1st, 2022
supremum-and-infimum
notation
Rudin Theorem $1.11$
August 1st, 2022
supremum-and-infimum
order-theory
analysis
real-analysis
upper-lower-bounds
Simple explanation of uniform norm / sup-norm?
August 1st, 2022
supremum-and-infimum
normed-spaces
The Supremum and Infimum of a sequence of measurable functions is measurable
August 1st, 2022
elementary-set-theory
measure-theory
supremum-and-infimum
$\liminf$ of a sequence of functions
August 1st, 2022
functions
limsup-and-liminf
supremum-and-infimum
sequences-and-series
Why is the lagrange dual function concave?
April 15th, 2021
supremum-and-infimum
lagrange-multiplier
To show that the supremum of any collection of lower semicontinuous functions is lower semicontinuous
August 1st, 2022
general-topology
continuity
semicontinuous-functions
supremum-and-infimum
Convex function can be written as supremum of some affine functions
October 10th, 2020
real-analysis
convex-analysis
supremum-and-infimum
Prove that the sum of the infima is smaller than the infimum of the sum
May 5th, 2021
supremum-and-infimum
inequality
real-analysis
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