# sigfpe

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bio website blog.sigfpe.com location age member for 2 years, 10 months seen May 7 at 21:02 profile views 117

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 Oct8 comment Seemingly simple system of equationsIf you know that 6 is a root then divide x-6 into your cubic (en.wikipedia.org/wiki/Polynomial_long_division) You'll be left with a quadratic that's easy to solve. Oct6 awarded Student Oct6 asked Numerical optimisation in presence of fast algorithm for some axes Jul21 awarded Yearling Jan18 comment Probability of picking a random natural numberThis is more a question for a psychologist than for a mathematician. Humans tend to pick certain numbers more often than other numbers. For example 7, 17, 35 and 37 are quite popular. No amount of mathematics would allow you to predict such a distribution without some facts from psychology. See here for some more details: scienceblogs.com/cognitivedaily/2007/02/… Jan18 comment Odds of Winning the Lottery Using the Same Numbers Repeatedly Better/Worse?@afilbert It's a bad idea to play pet numbers. Pet numbers are numbers that are special to you for some reason. The set of numbers that are special to people is much smaller than the set of all possible numbers. (Eg. people often pick dates which means 19 comes up often in people's pet numbers.) The net effect is that you are more likely to choose the same combination as someone else and have to share the prize. Pick randomly instead. And don't just pick numbers as people often pick the same 'random' numbers (eg. 37 is popular). Dec11 awarded Quorum Aug13 awarded Commentator Aug13 comment Is the Subset Axiom Schema in ZF necessary?In response to 3. The subset axiom schema says we can make sets by finding all elements of another set that satisfy a predicate. It doesn't "allow only" these subsets because it doesn't say that there aren't other types of subset as well. Aug1 awarded Enlightened Jul27 awarded Beta Jul26 awarded Nice Answer Jul22 comment If all sets were finite, how could the real numbers be defined?@Noldorin You are simply plain wrong. @Mgccl gives a perfectly good example of how you can reason about e using finite methods. You can prove things about e using finite machines running for a finite amount of time. You can reason about machines using finite mathematics. You don't need "the concept of infinity". Jul22 comment If all sets were finite, how could the real numbers be defined?@Noldorin Firstly, constructivism isn't normally opposed to intuitionism. Constructivism and intuitionism (which are closely related) are opposed to classical mathematics. And this is only tangentially related. You can reason about (some) real numbers, using the naturals, by interpreting statements about real numbers as being statements about natural numbers in disguise. You can even reason about (some) infinite sets this way using Peano arithmetic. This mentions the encoding of infinite ordinals up to $\epsilon_0$ as finite objects: en.wikipedia.org/wiki/Peano_axioms#Consistency Jul22 awarded Editor Jul22 revised If all sets were finite, how could the real numbers be defined?added 802 characters in body; added 7 characters in body; added 2 characters in body Jul22 comment If all sets were finite, how could the real numbers be defined?@Noldorin You are confusing two things. There is the set of real numbers and the real numbers themselves. You could not construct the set of real numbers, but you can still reason about real numbers by not constructing sets of them. In Peano arithmetic you can make statements about all of the natural numbers despite there being no set of all natural numbers. The same goes for some statements about real numbers. Jul22 comment If all sets were finite, how could the real numbers be defined?@Noldorin Statements about real numbers can be unpacked as statements about naturals. For example, stating that $\sqrt{2}$ is irrational can be unpacked as a statement that given a rational approximation to $\sqrt{2}$ (a notion that can be defined using just naturals) you can always find a better approximation, but never an exact solution to $a^2=2b^2$. Jul22 answered If all sets were finite, how could the real numbers be defined? Jul21 comment Do complex numbers really exist?The granularity of quantum mechanics is observed regularly, and fairly directly, in the lab. It's far more 'real' than the complex numbers.