Francesco
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 2d comment Great mathematics! I recommend "what is mathematics" by Courant. It will provide you with a fascinating tour of many ideas. 2d comment Brostein Integral 21.42 This is something that I used to know, but the proof of it is escaping me at the moment. The result is sound, suppose a >> b, you collect a^2 which gives you 2 \pi log a + a "residual integral". Now you have to prove that the residual integral is really zero... I 'll continue to think about it. Aug 3 comment How to recognise intuitively which functions grow faster asymptotically? @nbro there's no need to come up with the reverse reasoning: $log(n)^{log(n)} = exp\{log( log(n)^{log(n)})\} = exp\{log(n) * log(log(n))\}= exp\{log(n)\}^{log(log(n))} = n^{log(log(n))}$ May 16 comment What's the difference between arccos(x) and sec(x) And now you are ready for: "the derivative of the inverse is the inverse of the derivative" :-) Jun 8 comment Is it generally accepted that if you throw a dart at a number line you will NEVER hit a rational number? @Lubin as a physicist I would say that the problem is more with confusing "low probability" with "impossible", rather than "measure zero" with "impossible". But keep in mind that physicist usually handle low probabilities well enough (think of computation involving quantum mechanical crossing of barriers). And physicist often also handle the subtleties of hypothesis testing reasonably well. Now, surely "often" doesn't mean that the set of cases where some error may happen has measure zero :-) Feb 26 comment Show that $\tan 3x =\frac{ \sin x + \sin 3x+ \sin 5x }{\cos x + \cos 3x + \cos 5x}$ A. Raina: it isn't nice to make one feel old :-) I don't want even to think about how many years have lapsed since I studied prostaphaeresis: en.wikipedia.org/wiki/Prosthaphaeresis Feb 21 comment Examples of apparent patterns that eventually fail This was exactly the example that I was going to give, +1 from me Feb 6 comment Prove that $n! > \sqrt{n^n}, n \geq 3$ I don't find the "growth factor" approach ugly, since it provides a technique adaptable to other cases. +1 from me. Oct 11 comment Seeking a layman's guide to Measure Theory I enjoyed his style of writing and his approach to the matter, so I felt justified in suggesting it. But of course other books are valid alternatives.