List questions from monotone-functions

Published on 27 Aug 2018 - 17:15

420

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Is every monotonic additive function $f \colon \mathbb{R} \to \mathbb{R}$ continuous?

Published on 05 Sep 2018 - 11:17

228

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Definition 5.6.6 in Bartle & Sherbert's INTRO TO REAL ANALYSIS: How to show that this notion is well-defined?

Published on 06 Sep 2018 - 9:15

328

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Prob. 6, Sec. 5.6, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: A necessary and sufficient condition for continuity of a monotonic function

Published on 07 Sep 2018 - 8:32

96

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continuous and monotonous implies almost differentiable

Published on 13 Sep 2018 - 15:28

158

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Proving monotonicity

Published on 17 Sep 2018 - 10:51

1k

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Is k=$\sqrt{6+\sqrt{6+...}}$ monotonically increasing?

Published on 23 Sep 2018 - 16:20

264

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Monotonic transformation to smooth the probabilities

Published on 22 Mar 2026 - 19:18

219

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If $a_n=\Theta(b_n)$, does this imply that $a_n/b_n\to c$ with $c>0$ as $n\to\infty$?

Published on 11 Oct 2018 - 7:46

336

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Find range of exponent

Published on 11 Oct 2018 - 9:29

87

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Show that a function cannot be expressed as a strictly increasing transformation of another function

Published on 16 Oct 2018 - 18:09

81

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Another examples of strictly monotone surjective function from an interval to another interval

Published on 17 Oct 2018 - 18:35

1.2k

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Notation: "is a monotonic function of"?

Published on 17 Oct 2018 - 19:50

121

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Injectivity proof

Published on 18 Oct 2018 - 14:12

22

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Injectivity parameter

Published on 18 Oct 2018 - 21:23

List Question

Prove that a sequence converges monotonically to the solution of an equation.

Is every monotonic additive function $f \colon \mathbb{R} \to \mathbb{R}$ continuous?

Definition 5.6.6 in Bartle & Sherbert's INTRO TO REAL ANALYSIS: How to show that this notion is well-defined?

Prob. 6, Sec. 5.6, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: A necessary and sufficient condition for continuity of a monotonic function

continuous and monotonous implies almost differentiable

Proving monotonicity

Is k=$\sqrt{6+\sqrt{6+...}}$ monotonically increasing?

Monotonic transformation to smooth the probabilities

If $a_n=\Theta(b_n)$, does this imply that $a_n/b_n\to c$ with $c>0$ as $n\to\infty$?

Find range of exponent

Show that a function cannot be expressed as a strictly increasing transformation of another function

Another examples of strictly monotone surjective function from an interval to another interval

Notation: "is a monotonic function of"?

Injectivity proof

Injectivity parameter

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