List questions from alternative-proof

Published on 15 Oct 2016 - 16:56

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If $f''(x)+2f'(x)+3f(x)=0$, then $f$ is infinitely differentiable

Published on 16 Oct 2016 - 0:12

155

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Can we prove summation formula for the first $n$ terms of natural numbers through calculus?

Published on 16 Oct 2016 - 0:51

502

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Jacobian of an inverse coordinate transformation

Published on 17 Oct 2016 - 4:02

5.1k

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Let $f$ be a real uniformly continuous function on the bounded set $E$ in $\mathbb{R^1}$. Prove that $f$ is bounded on $E$

Published on 19 Oct 2016 - 7:58

277

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Limit of $\left\{ \int_{0}^{1} [bx + a(1 - x) ]^{\frac1n} dx \right\}^n$ as $n \to \infty$

Published on 03 Apr 2026 - 12:36

1.1k

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Proof of $\mathrm{dim}(U)\leq \mathrm{dim}(V)$ if $U$ is a subspace of $V$

Published on 21 Oct 2016 - 3:40

116

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Can we simplify this proof?

Published on 22 Oct 2016 - 22:27

37

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Is this proof valid for $A\subset B \implies A \cap B = A$?

Published on 22 Oct 2016 - 22:34

114

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Can't prove the base case for an induction proof

Published on 01 Apr 2026 - 7:50

181

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About theorems on nowhere dense set

Published on 23 Oct 2016 - 11:46

592

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Proof-method: Show that if $n$ is not prime then $\Bbb Z /n\Bbb Z$ is not a field

Published on 23 Oct 2016 - 19:33

87

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Is there a better way to explain why $\phi \left ( p^k \right ) = p^k - p^{k-1}$?

Published on 24 Oct 2016 - 13:53

268

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Do we need the axiom of choice to prove L'Hopital's rule?

Published on 01 Apr 2026 - 10:24

42

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Prove that $L(C_x)=L(C_y)$ when $I(C_x)=I(C_y)$

Published on 26 Oct 2016 - 15:37

List Question

Combinatorial question regarding size of subsets of pairs

If $f''(x)+2f'(x)+3f(x)=0$, then $f$ is infinitely differentiable

Can we prove summation formula for the first $n$ terms of natural numbers through calculus?

Jacobian of an inverse coordinate transformation

Let $f$ be a real uniformly continuous function on the bounded set $E$ in $\mathbb{R^1}$. Prove that $f$ is bounded on $E$

Limit of $\left\{ \int_{0}^{1} [bx + a(1 - x) ]^{\frac1n} dx \right\}^n$ as $n \to \infty$

Proof of $\mathrm{dim}(U)\leq \mathrm{dim}(V)$ if $U$ is a subspace of $V$

Can we simplify this proof?

Is this proof valid for $A\subset B \implies A \cap B = A$?

Can't prove the base case for an induction proof

About theorems on nowhere dense set

Proof-method: Show that if $n$ is not prime then $\Bbb Z /n\Bbb Z$ is not a field

Is there a better way to explain why $\phi \left ( p^k \right ) = p^k - p^{k-1}$?

Do we need the axiom of choice to prove L'Hopital's rule?

Prove that $L(C_x)=L(C_y)$ when $I(C_x)=I(C_y)$

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