Categories
Tags
Examples-counterexamples
New post in Examples-counterexamples
An example of a martingale converge almost surely but not in $L^1$?
March 24th, 2020
examples-counterexamples
probability-theory
martingales
Example of when the minimum of two convex functions is not convex
August 1st, 2022
convex-optimization
convex-analysis
maxima-minima
examples-counterexamples
Counterexample to inverse Leibniz alternating series test
August 1st, 2022
examples-counterexamples
real-analysis
sequences-and-series
Are there any examples of Graphs in nature?
August 1st, 2022
examples-counterexamples
graph-theory
If $a, b$ are relatively prime proof and $ab$ is a perfect square, so are $a$, $b$
August 1st, 2022
examples-counterexamples
elementary-number-theory
square-numbers
proof-writing
Is it true that if $x_n$ converges and $y_n$ is bounded, then $x_ny_n$ converges?
August 1st, 2022
real-analysis
examples-counterexamples
proof-verification
Product of concave functions is concave
April 10th, 2021
functions
examples-counterexamples
convex-analysis
If $f$ is continuous and $X$ is locally compact, then $f(X)$ is locally compact.
August 1st, 2022
compactness
continuity
general-topology
examples-counterexamples
Continuous or Differentiable but Nowhere Lipschitz Continuous Function
August 1st, 2022
lipschitz-functions
real-analysis
continuity
examples-counterexamples
fractals
Functions $\mathbb{N} \to \mathbb{N}$ that are injective but not surjective, and vice versa
August 1st, 2022
elementary-set-theory
functions
examples-counterexamples
Differentiable continuous function whose derivative is not continuous
August 1st, 2022
derivatives
continuity
examples-counterexamples
real-analysis
calculus
prove or disprove that $CL(A∩B)=CL(A)∩CL(B)$
August 1st, 2022
general-topology
examples-counterexamples
If $\sum a_n$ with $a_n>0$ is convergent, then is $\sum {a_n}^2$ and $\sum \sqrt{a_n}$ always convergent?
August 1st, 2022
examples-counterexamples
sequences-and-series
real-analysis
Method to determine if a ring is a UFD?
August 1st, 2022
unique-factorization-domains
ring-theory
examples-counterexamples
normed-spaces
Example of a metric space first countable but not second countable.
June 5th, 2020
general-topology
examples-counterexamples
analysis
A $T_1$ space which is not Hausdorff
September 24th, 2020
examples-counterexamples
general-topology
What are some examples of infinite nonabelian groups?
August 1st, 2022
abelian-groups
infinite-groups
big-list
group-theory
examples-counterexamples
second derivative does not exist at specified points
June 5th, 2020
real-analysis
derivatives
examples-counterexamples
Function with infinitely many right inverses?
August 1st, 2022
examples-counterexamples
inverse-function
functions
elementary-set-theory
Divergent series whose terms converge to zero
August 1st, 2022
calculus
sequences-and-series
examples-counterexamples
convergence-divergence
Which function ($f$) is continuous nowhere but $|f(x)|$ is continuous everywhere?
August 1st, 2022
continuity
examples-counterexamples
absolute-value
calculus
In-depth example or implementation of adaptive control (direct/indirect MRAC)?
August 1st, 2022
adaptive-control
control-theory
examples-counterexamples
Convergence of Monotone sequences? example
November 14th, 2020
convergence-divergence
sequences-and-series
real-analysis
examples-counterexamples
Example of a continuous non-lipschitz function with domain $[0,1]$ and co-domain $\mathbb R$
August 1st, 2022
functions
examples-counterexamples
lipschitz-functions
continuity
calculus
An example in Cantor's intersection theorem if the hypothesis $\text{diam}(D_n)\to0$ as $n\to\infty$ is omitted
August 1st, 2022
metric-spaces
convergence-divergence
examples-counterexamples
Inequalities on greatest integer function
August 1st, 2022
inequality
ceiling-and-floor-functions
examples-counterexamples
Listing all the distinct left cosets
November 21st, 2020
examples-counterexamples
abstract-algebra
Non-existence of bijective, continuous function from $(0,1)$ to $[0,1]$
June 3rd, 2020
examples-counterexamples
continuity
real-analysis
Greedy algorithm fails to give chromatic number
August 1st, 2022
graph-theory
examples-counterexamples
coloring
Infinite sum of random variables is infinite
August 1st, 2022
examples-counterexamples
probability-theory
measure-theory
probability
←
1
2
3
4
5
6
7
8
9
…
24
25
→