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 Mar 30 comment Is this function really not concave or convex in any range? @MichaelGrant thanks - so the fact that the graph looks concave for example in $x<-5; y>0.5$ is basically just an "optical illusion"? Mar 29 revised Is this function really not concave or convex in any range? edited title Mar 29 revised Is this function really not concave or convex in any range? added 30 characters in body Mar 29 asked Is this function really not concave or convex in any range? Mar 10 accepted Composition of non-monotonic convex function Mar 10 accepted Use $\log(x)$ to calculate $\log(x+1)$ Mar 10 asked Log-concave function changes when scalar is added Mar 10 comment In simple English, what does it mean to be transcendental? Wikipedia has a feature called "Simple English", the description there is very short but reasonable: simple.wikipedia.org/wiki/Transcendental_number Feb 2 comment Is there a name for subtracting a set of values from their max? Thanks - is there any specific reason behind this term? Is it used elsewhere? Feb 2 comment Use $\log(x)$ to calculate $\log(x+1)$ @Winther using python/numpy, which has builtin $log()$, $log1p()$ etc. Feb 2 comment Use $\log(x)$ to calculate $\log(x+1)$ @Winther application - I may need to sum 10^9 such values to calculate a partition function. Feb 2 comment Use $\log(x)$ to calculate $\log(x+1)$ @BrianTung double precision. Feb 2 asked Use $\log(x)$ to calculate $\log(x+1)$ Dec 14 comment How to find that $x^2 +y^2=z^2$ describes an infinite cone by simple algebra manipulation and change of coordinates? Yes, this is how I see it. In the original equation the radius increases as $z$ increases. Dec 14 comment How to find that $x^2 +y^2=z^2$ describes an infinite cone by simple algebra manipulation and change of coordinates? Are you just looking for an intuitive explanation? Can you see why $x^2 +y^2 = r^2$ is a circle with radius $r$? The cone follows from there. Dec 10 comment If we randomly select 25 integers between 1 and 100, how many consecutive integers should we expect? +1 for the most useful answer. I think what OP really wants to know is: given that I see $x$ pairs, what is the probability of this happening by chance? (either this or a p-value version, i.e. $x$ or more). Sep 21 awarded Yearling Jun 5 awarded Nice Question Jun 4 comment Is there a term for the ratio of a function and its derivative? Thanks - this is actually how I got this ratio in the first place. Jun 4 accepted Is there a term for the ratio of a function and its derivative?