List questions from proof-verification

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Matrix function is continuous iff its components are continuous

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Proving That $f: \mathbb{Z} \to \mathbb{Z}$, where $f(x) = x + 10$, Is Surjective

Published on 02 Apr 2018 - 17:19

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Prove the following inequality by Induction

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Evaluating the integral $\int_{\partial\Bbb D}\frac{e^z\sin z}{(1-e^z)^2}\, dz$

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Getting a contradiction based on assumption?

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Is this proof that every strictly increasing $f\colon\mathbb{R\to R}$ is injective flawed?

Published on 03 Apr 2018 - 1:51

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Real Analysis Sequence limit

Published on 03 Apr 2018 - 2:39

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Proof- Disjointed open sets in $\mathbb{R}$ are separated.

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CDF of Chi-square distribution

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Showing that a harmonic function maps open sets to open sets.

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Prove that this function is NOT differentiable at $c=0$.

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The proof of: If $V$ is generated by a finite set $S$, then some subset of $S$ is a basis for $V$.

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If $g \circ f$ is injective and $f$ is surjective, then $g$ is injective.

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"Strange" isomorphism $\mathbb C^/C_n\simeq \mathbb C^$

Published on 03 Apr 2018 - 18:47

List Question

Prove: $\det(\alpha v_1,v_2,\dots v_n)=\alpha\cdot \det(v_1,v_2,\dots v_n)$

Matrix function is continuous iff its components are continuous

Proving That $f: \mathbb{Z} \to \mathbb{Z}$, where $f(x) = x + 10$, Is Surjective

Prove the following inequality by Induction

Evaluating the integral $\int_{\partial\Bbb D}\frac{e^z\sin z}{(1-e^z)^2}\, dz$

Getting a contradiction based on assumption?

Is this proof that every strictly increasing $f\colon\mathbb{R\to R}$ is injective flawed?

Real Analysis Sequence limit

Proof- Disjointed open sets in $\mathbb{R}$ are separated.

CDF of Chi-square distribution

Showing that a harmonic function maps open sets to open sets.

Prove that this function is NOT differentiable at $c=0$.

The proof of: If $V$ is generated by a finite set $S$, then some subset of $S$ is a basis for $V$.

If $g \circ f$ is injective and $f$ is surjective, then $g$ is injective.

"Strange" isomorphism $\mathbb C^/C_n\simeq \mathbb C^$

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