Question

If $f:[0,1] \longrightarrow \mathbb{R}$ is $C^{\infty}$, can we say that it is positive or negative?

score 50 · Answer 1 · 2015-10-07 12:43:38

50

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If $f:[0,1] \longrightarrow \mathbb{R}$ is $C^{\infty}$, can we say that it is positive or negative?

Published on 07 Oct 2015 - 12:43

score 1.5k · Answer 2 · 2015-10-07 13:12:26

1.5k

Views

Given that $x,y,z$ are positive reals such that $xyz=32$.What is the minimum value of $x^2+4xy+4y^2+2z^2$.

Published on 07 Oct 2015 - 13:12

score 7.4k · Answer 3 · 2026-04-02 17:42:57

7.4k

Views

supremum and limsup of random variables

Published on 02 Apr 2026 - 17:42

score 283 · Answer 4 · 2015-10-08 16:40:42

283

Views

supremum and infimum of set $\left\{ \frac{nk}{1+2n+3k} : n,k \in \mathbb{N} \right\}$

Published on 08 Oct 2015 - 16:40

score 97 · Answer 5 · 2026-02-25 12:42:37

97

Views

Inf and Sup question

Published on 25 Feb 2026 - 12:42

score 9.4k · Answer 6 · 2026-04-01 00:51:56

9.4k

Views

proving if $a \le b$ then $\sup(A) \le \inf(B)$

Published on 01 Apr 2026 - 0:51

score 9.3k · Answer 7 · 2026-04-02 12:26:54

9.3k

Views

Proving the nested interval theorem

Published on 02 Apr 2026 - 12:26

score 220 · Answer 8 · 2026-03-23 03:52:05

220

Views

Confused about my professor's answer for an inf and sup question

Published on 23 Mar 2026 - 3:52

score 357 · Answer 9 · 2015-10-12 22:14:33

357

Views

The Limit, supremum and infimum of a set.

Published on 12 Oct 2015 - 22:14

score 203 · Answer 10 · 2015-10-13 08:27:51

203

Views

Example 13, Sec. 3 in Munkres' TOPOLOGY, 2nd ed: Necessary and Sufficient Conditions for a Subset to Have the Least Upper Bound Property

Published on 13 Oct 2015 - 8:27

score 201 · Answer 11 · 2026-04-01 00:52:53

201

Views

Proving $\sup \{|x_j-y_j|: j\in \mathbb{N}\}$ is a distance metric for bounded sequences of reals

Published on 01 Apr 2026 - 0:52

score 121 · Answer 12 · 2026-03-12 14:12:32

121

Views

Proof of supremum and infemum of bounded functions

Published on 12 Mar 2026 - 14:12

score 50 · Answer 13 · 2015-10-15 18:59:21

50

Views

How to show $\epsilon > \frac{3^n -1}{n! + 124} > \frac{1}{n!}$

Published on 15 Oct 2015 - 18:59

score 2k · Answer 14 · 2026-03-28 12:36:25

2k

Views

Bound on the difference of infimums

Published on 28 Mar 2026 - 12:36

score 40 · Answer 15 · 2015-10-17 10:25:53

40

Views

Proof of convergence implication

Published on 17 Oct 2015 - 10:25

List Question

If $f:[0,1] \longrightarrow \mathbb{R}$ is $C^{\infty}$, can we say that it is positive or negative?

Given that $x,y,z$ are positive reals such that $xyz=32$.What is the minimum value of $x^2+4xy+4y^2+2z^2$.

supremum and limsup of random variables

supremum and infimum of set $\left\{ \frac{nk}{1+2n+3k} : n,k \in \mathbb{N} \right\}$

Inf and Sup question

proving if $a \le b$ then $\sup(A) \le \inf(B)$

Proving the nested interval theorem

Confused about my professor's answer for an inf and sup question

The Limit, supremum and infimum of a set.

Example 13, Sec. 3 in Munkres' TOPOLOGY, 2nd ed: Necessary and Sufficient Conditions for a Subset to Have the Least Upper Bound Property

Proving $\sup \{|x_j-y_j|: j\in \mathbb{N}\}$ is a distance metric for bounded sequences of reals

Proof of supremum and infemum of bounded functions

How to show $\epsilon > \frac{3^n -1}{n! + 124} > \frac{1}{n!}$

Bound on the difference of infimums

Proof of convergence implication

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