List questions from examples-counterexamples

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If $g(n) \neq O(f(n))$, is $g(n) = \Omega(f(n))$?

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How do we prove that $\lfloor0.999\cdots\rfloor = \lfloor 1 \rfloor$?

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Gluing Lemma for Closed Sets: Infinite Cover Counter-Example

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Examples of Topological Embeddings and Quotient Maps

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If $A^2 = I$ (Identity Matrix) then $A = \pm I$

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Counterexample for graph isomorphism using eigenvalue multiplicity (connected graphs)

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$(0,1)\to\mathbb{R}^2$ injective, continuous, not a homeomorphism on the image

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Examples of reductive groups of dimension $4$ and semisimple rank $1$

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Distinct metrics on a manifold

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Give an example of a homogeneous, but not strongly homogeneous model

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Example of height $n$ ideal with $I/I^2$ (locally) $n$-generated, but $I$ is not.

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Endomorphism ring which is not the endomorphism ring of an abelian group.

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Examples of patterns that eventually fail

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How discontinuous can a derivative be?

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List Question

Counterexamples to the converse to Lagrange's Theorem different from $A_{4}$.

If $g(n) \neq O(f(n))$, is $g(n) = \Omega(f(n))$?

How do we prove that $\lfloor0.999\cdots\rfloor = \lfloor 1 \rfloor$?

Gluing Lemma for Closed Sets: Infinite Cover Counter-Example

Examples of Topological Embeddings and Quotient Maps

If $A^2 = I$ (Identity Matrix) then $A = \pm I$

Counterexample for graph isomorphism using eigenvalue multiplicity (connected graphs)

$(0,1)\to\mathbb{R}^2$ injective, continuous, not a homeomorphism on the image

Examples of reductive groups of dimension $4$ and semisimple rank $1$

Distinct metrics on a manifold

Give an example of a homogeneous, but not strongly homogeneous model

Example of height $n$ ideal with $I/I^2$ (locally) $n$-generated, but $I$ is not.

Endomorphism ring which is not the endomorphism ring of an abelian group.

Examples of patterns that eventually fail

How discontinuous can a derivative be?

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