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 Jul 11 comment Is there a sequence in $(0,1)$ such that the product of all its terms is $\frac{1}{2}$? I like the telescoping product, too. Jul 10 comment Is there a sequence in $(0,1)$ such that the product of all its terms is $\frac{1}{2}$? As long as the sequence $\pi_n$ is positive and strictly decreasing. Jul 7 comment Kolmogorov's unit interval probability space That's right! Now I remember! Thanks for reminding me. That was ages ago and I must have forgotten. It's been 14 years since I took probability. Jul 7 comment Can we possibly combine $\int_a^b{g(x)dx}$ plus $\int_c^d{h(x)dx}$ into $\int_e^f{j(x)dx}$? Maybe it will help to look at it like this: we are setting $$\frac{u-a}{b-a}=\frac{v-c}{d-c}=\frac{x-e}{f-e}$$ and allowing each of these fractions to range from 0 to 1. Jul 7 comment Can we possibly combine $\int_a^b{g(x)dx}$ plus $\int_c^d{h(x)dx}$ into $\int_e^f{j(x)dx}$? I think you might have those fractions upside-down. Shouldn't you get $x=\frac{f-e}{b-a}(u-a)+e$ and $dx=\frac{f-e}{b-a}du$? But you don't really need to do that anyways. Just express $u$, $du$, $v$, and $dv$ in terms of $x$ and $dx$, and plug those substitutions into the first two integrals. Jul 7 comment Can we possibly combine $\int_a^b{g(x)dx}$ plus $\int_c^d{h(x)dx}$ into $\int_e^f{j(x)dx}$? @MattGroff: try working out the change of variables I indicated in an edit to my answer. Jul 6 comment Learning math-oriented French For some reason the French like to denote an open interval by $]a,b[$ instead of $(a,b)$ and they put a lot of space between an equation and any grammatical punctuation. Probability distributions are still called "lois" in French, which comes across as somewhat quaint and old-fashioned in English. Read some of the papers at numdam.org just to get a feel for the language. Jul 2 comment Roman numerals Subtractive VS Additive Just as an example for subtractive notation, 1999 is not generally written "IM", as might be supposed, but rather "MCMXCIX".