Question

Generalized Pythagorean integer solutions

score 131 · Answer 1 · 2026-03-26 17:52:17

131

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Generalized Pythagorean integer solutions

Published on 26 Mar 2026 - 17:52

score 131 · Answer 2 · 2018-07-26 23:44:15

131

Views

Show, using the definition of derivative, that $f:\mathbb{R}^2\rightarrow\mathbb{R}$ defined by $f(x,y)=xy$ is differentiable everywhere.

Published on 26 Jul 2018 - 23:44

score 146 · Answer 3 · 2026-03-25 13:56:28

146

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Where did I go wrong in my working? - integration via substitution $\int_{0}^{\frac{1}{2}\ln3}\frac{1}{e^x+e^{-x}}dx$.

Published on 25 Mar 2026 - 13:56

score 110 · Answer 4 · 2018-07-27 02:44:01

110

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Is the application of Lebesgue DCT valid here?

Published on 27 Jul 2018 - 2:44

score 2.2k · Answer 5 · 2018-07-27 03:58:35

2.2k

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Proof that if $n^2-1$ is divisible by $8$ then $n$ is odd

Published on 27 Jul 2018 - 3:58

score 1k · Answer 6 · 2026-03-25 13:55:23

1k

Views

Show that any right angled triangle with hypotenuse 1 may be approximated arbitrarily close by one with rational sides

Published on 25 Mar 2026 - 13:55

score 649 · Answer 7 · 2026-03-25 11:16:34

649

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Prob. 1, Sec. 25, in Munkres' TOPOLOGY, 2nd ed: The components and the path components of $\mathbb{R}$ with lower limit topology

Published on 25 Mar 2026 - 11:16

score 45 · Answer 8 · 2018-07-27 16:24:31

45

Views

Understanding continuity and Dense sets

Published on 27 Jul 2018 - 16:24

score 852 · Answer 9 · 2018-07-27 19:21:35

852

Views

For all integers $n$: if $7n+4$ is even, then $5n+6$ is even.

Published on 27 Jul 2018 - 19:21

score 425 · Answer 10 · 2026-03-25 11:16:41

425

Views

Prob. 2(b), Sec. 25, in Munkres' TOPOLOGY, 2nd ed: The iff-condition for two points to be in the same component of $\mathbb{R}^\omega$

Published on 25 Mar 2026 - 11:16

score 81 · Answer 11 · 2018-07-27 21:17:48

81

Views

Where is my error in this proof that the uniform limit of Riemann integrable functions is Riemann integrable?

Published on 27 Jul 2018 - 21:17

score 4k · Answer 12 · 2026-03-25 16:08:27

4k

Views

Show that the $\lim \inf a_n = \lim \sup a_n$ if and only if $\lim a_n$ exists.

Published on 25 Mar 2026 - 16:08

score 71 · Answer 13 · 2026-03-28 02:42:03

71

Views

Koszul complex via alternating functions

Published on 28 Mar 2026 - 2:42

score 37 · Answer 14 · 2018-07-27 23:20:16

37

Views

Where did I go wrong in my integration (by parts)?

Published on 27 Jul 2018 - 23:20

score 63 · Answer 15 · 2018-07-28 00:28:33

63

Views

Prove $\lim_{(h,k)\to 0} \dfrac{|f(h,k)|}{|(h,k)|}=0$ for bilinear $f$

Published on 28 Jul 2018 - 0:28

List Question

Generalized Pythagorean integer solutions

Show, using the definition of derivative, that $f:\mathbb{R}^2\rightarrow\mathbb{R}$ defined by $f(x,y)=xy$ is differentiable everywhere.

Where did I go wrong in my working? - integration via substitution $\int_{0}^{\frac{1}{2}\ln3}\frac{1}{e^x+e^{-x}}dx$.

Is the application of Lebesgue DCT valid here?

Proof that if $n^2-1$ is divisible by $8$ then $n$ is odd

Show that any right angled triangle with hypotenuse 1 may be approximated arbitrarily close by one with rational sides

Prob. 1, Sec. 25, in Munkres' TOPOLOGY, 2nd ed: The components and the path components of $\mathbb{R}$ with lower limit topology

Understanding continuity and Dense sets

For all integers $n$: if $7n+4$ is even, then $5n+6$ is even.

Prob. 2(b), Sec. 25, in Munkres' TOPOLOGY, 2nd ed: The iff-condition for two points to be in the same component of $\mathbb{R}^\omega$

Where is my error in this proof that the uniform limit of Riemann integrable functions is Riemann integrable?

Show that the $\lim \inf a_n = \lim \sup a_n$ if and only if $\lim a_n$ exists.

Koszul complex via alternating functions

Where did I go wrong in my integration (by parts)?

Prove $\lim_{(h,k)\to 0} \dfrac{|f(h,k)|}{|(h,k)|}=0$ for bilinear $f$

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