Tag: real-analysis

170 Have any long-suspected irrational numbers turned out to be rational? 2010-07-22T16:06:17.797

148 If $f$ is infinitely differentiable then $f$ coincides with a polynomial 2010-07-31T21:37:22.197

98 Why is differentiating mechanics and integration art? 2011-05-29T16:44:52.087

92 integral of a "sin-omial" coefficients=binomial 2016-11-02T00:25:27.553

84 solving $f(f(x))=g(x)$ 2010-03-09T15:40:09.837

84 Why do we teach calculus students the derivative as a limit? 2010-09-27T05:29:56.663

73 Does there exist a bijection of $\mathbb{R}^n$ to itself such that the forward map is connected but the inverse is not? 2016-04-11T14:56:13.680

69 If I exchange infinitely many digits of $\pi$ and $e$, are the two resulting numbers transcendental? 2017-03-23T01:06:13.370

68 Proofs of the uncountability of the reals. 2010-11-22T17:19:28.037

66 Why is Lebesgue integration taught using positive and negative parts of functions? 2010-05-18T18:29:17.903

66 Does pointwise convergence imply uniform convergence on a large subset? 2010-11-12T04:01:44.457

61 f(f(x))=exp(x)-1 and other functions "just in the middle" between linear and exponential 2009-11-06T07:29:36.680

61 Is the series $\sum_n|\sin n|^n/n$ convergent? 2017-09-28T18:24:46.760

60 Taking "Zooming in on a point of a graph" seriously 2011-10-04T20:48:00.483

55 Continuous maps which send intervals of $\mathbb{R}$ to convex subsets of $\mathbb{R}^2$ 2015-03-20T14:16:55.223

54 Why do functions in complex analysis behave so well? (as opposed to functions in real analysis) 2009-11-02T17:22:52.617

52 Square root of dirac delta function 2016-04-10T14:49:45.767

49 When has the Borel-Cantelli heuristic been wrong? 2015-04-15T20:31:08.947

49 Why does $d^n \exp(-x-x^{-1})/(dx)^n$ only have $n$ positive real zeroes? 2015-08-19T15:45:34.000

47 Is a function with nowhere vanishing derivatives analytic? 2013-12-25T22:45:11.533

45 Why could Mertens not prove the prime number theorem? 2012-05-02T10:03:24.657

43 The missing link: an inequality 2017-01-09T22:40:03.737

41 "Closed-form" functions with half-exponential growth 2010-11-09T18:51:19.420

41 Every real function has a dense set on which its restriction is continuous 2011-08-12T23:28:54.530

40 Smooth functions for which $f(x)$ is rational if and only if $x$ is rational 2010-12-10T12:05:41.607

40 On an example of an eventually oscillating function 2015-02-27T19:49:34.980

38 The Hardy Z-function and failure of the Riemann hypothesis 2010-12-23T16:23:50.957

37 Are some numbers more irrational than others? 2011-01-29T16:11:17.737

37 Is the following identity true? 2016-06-08T14:04:01.487

35 Integrability of derivatives 2009-11-24T18:37:36.503

34 Everywhere differentiable function that is nowhere monotonic 2014-05-16T12:40:57.597

33 Interesting applications (in pure mathematics) of first-year calculus 2010-08-10T16:38:15.253

33 Square root of a positive $C^\infty$ function. 2012-08-25T02:25:35.587

33 Binomial again, and again 2016-11-17T03:21:03.647

32 Is $π$ definable in $(\Bbb R,0,1,+,×,<,\exp)$? 2013-07-13T22:52:06.423

32 Differentiable functions with discontinuous derivatives 2013-12-19T15:18:15.360

32 For which maps $S^1\to S^1$ is the winding number defined? 2014-04-12T07:17:06.513

31 Is square of Delta function defined somewhere? 2010-12-02T17:10:11.030

31 An Entropy Inequality 2013-07-31T21:03:44.543

31 Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$ 2014-02-13T11:43:19.660

30 What did Rolle prove when he proved Rolle's theorem? 2014-10-14T01:01:58.993

29 Is $\sum_{k=1}^{n} \sin(k^2)$ bounded by a constant $M$? 2015-03-27T17:46:53.400

29 How quickly can the derivative of an everywhere differentiable function change sign? 2017-04-04T16:11:09.633

29 Wanted: Positivity certificate for the AM-GM inequality in low dimension 2017-08-30T16:26:27.370

28 Can Cantor set be the zero set of a continuous function? 2010-05-09T17:57:46.683

28 Function satisfying $f^{-1} =f'$ 2010-07-31T19:57:06.537

28 Continuous relations? 2014-08-22T17:00:39.867

27 Is pi = log_a(b) for some integers a, b > 1? 2013-01-10T11:37:22.463

27 Continuous functions $f$ with $f(A)$ linearly independent when $A$ is independent 2013-11-18T10:44:27.167

26 is f a polynomial provided that it is "partially" smooth? 2012-04-14T15:50:41.720

25 Text for an introductory Real Analysis course. 2009-11-04T00:44:34.510

25 For a continuous function $f:\mathbb{R}^{+}\to\mathbb{R}^{+}$ does $(f(x)-f(y)) (f(\frac{x+y}{2}) - f(\sqrt{xy}))=0$ imply that $f$ is constant? 2017-05-05T14:20:38.423

25 Polynomials non-negative on the integers 2017-07-20T06:43:58.953

24 $\binom{x}{2}+\binom{x}{4}+\cdots+\binom{x}{2u}$ is a convex function on $[0,+\infty)$? 2016-08-15T03:25:04.230

23 Is there a natural measures on the space of measurable functions? 2009-10-20T07:25:05.343

23 Rolle's theorem in n dimensions 2010-01-01T21:51:09.710

23 Does Arzelà-Ascoli require choice? 2010-11-13T15:14:52.803

23 Which ordered fields are homeomorphic to their power? 2014-11-29T11:48:51.693

22 Analogues of Luzin's theorem 2010-08-04T15:35:21.550

22 Codimension of Measurable Sets 2011-02-13T08:20:48.397

22 Asymptotics of a Selberg-type integral 2012-03-16T13:58:32.187

22 Classic applications of Baire category theorem 2013-05-04T18:27:15.027

22 Sum of Gaussian pdfs 2017-10-26T06:30:18.620

21 The role of the mean value theorem (MVT) in first-year calculus 2010-07-11T17:05:26.250

21 Function with range equal to whole reals on every open set 2010-07-16T07:05:46.777

21 Dual of bounded uniformly continuous functions 2010-10-29T21:20:17.850

21 Is a random subset of the real numbers non-measurable? Is the set of measurable sets measurable? 2012-07-16T20:21:25.607

21 Which smooth compactly supported functions are convolutions? 2014-02-05T19:34:12.407

21 Felix Klein on mean value theorem and infinitesimals 2014-02-13T15:31:27.713

21 Relative null-ness 2015-09-21T04:03:29.073

21 Evaluating an integral using real methods 2015-12-23T21:29:01.820

21 Does $a_n=\prod^n_{k=1}(1-e^{k\alpha \pi i})$ converge to zero when $\alpha$ is irrational? 2016-03-02T00:44:50.577

21 What is the set of all "pseudo-rational" numbers (see details)? 2017-01-14T06:51:59.030

21 Number of real roots of a polynomial 2017-02-01T19:54:25.987

20 Which is the correct ring of functions for a topological space? 2009-11-29T01:03:38.993

20 Prime ideals in the ring of germs of continuous functions 2011-11-15T22:36:25.180

20 a determinantal identity 2012-09-13T16:45:03.103

20 Is there a function defined on real numbers which is continuous from the left, but not from the right, everywhere 2013-11-14T11:04:18.317

20 A question about small sets of reals 2014-04-15T03:02:17.083

20 Minimum value of $|p(1)|^2+|p(2)|^2 +...+ |p(n+3)|^2$ over all monic polynomials $p$ 2015-07-04T16:18:47.463

20 Which partitions of $[0,1]$ are collection of level sets of a real continuous function? 2015-10-08T13:25:10.290

20 Kasteleyn's formula for domino tilings generalized? 2016-12-30T09:20:01.727

20 Bernoulli sum meets golden number 2017-06-15T00:59:49.823

20 What is the optimal speed to approach a red light? 2017-10-22T13:51:36.720

19 About the Riemann integrability of composite functions 2010-04-01T07:22:48.830

19 Convergence of Fourier Series of $L^1$ Functions 2010-06-16T19:08:02.170

19 Is a real power series that maps rationals to rationals defined by a rational function? 2010-10-17T05:41:14.920

19 Almost everywhere differentiability for a class of functions on $\mathbb{R}^2$ 2011-10-12T21:15:06.010

19 Constants for Rolle's Theorem applied to polynomials 2011-11-02T18:25:10.673

19 "Converse" of Taylor's theorem 2012-02-15T09:03:00.297

19 functions from Q to itself with derivative zero 2012-07-11T01:30:18.547

19 Counterexamples to differentiation under integral sign? 2012-08-28T22:54:30.880

19 Evaluation of an $n$-dimensional integral 2013-05-07T12:19:51.967

19 Is this statement which relates the Fourier transform of a function to its singularities correct? 2014-05-03T02:57:26.570

19 A Linear Order from AP Calculus 2015-08-27T16:12:46.250

19 A kaleidoscopic coloring of the plane 2015-10-02T18:55:32.703

19 mixing convex and concave for convexity 2016-08-06T03:11:31.590

18 Do convex and decreasing functions preserve the semimartingale property? 2010-10-23T17:25:31.007

18 If $f:R^n \to R$ is a smooth real-valued function such that $\nabla f : R^n \to R^n$ is a diffeomorphism, what can one conclude about the behavior of $f(x)$ at infinity? 2010-12-04T06:28:06.597