Dan Piponi
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 Aug5 comment In calculus, which questions can the naive ask that the learned cannot answer? First, you don't need table look-ups to compute elliptic integrals. There are a variety of methods for computing them. Second, in what sense can you not exactly calculate the arc-length of an ellipse but can exactly calculate the arc-length of a circle? Aug4 comment using the same symbol for dependent variable and function? This is a problematic area. Despite functions playing a central role in much of mathematics there isn't a clear unambiguous notation that mathematicians agree on. I think a good modern view is that $y$ is a function and $y(t)$ is the value of the function evaluated at $t$ in which case it (usually) makes no sense to say $y=y(t)$. But others take the view that $y=y(t)$ is a special use of notation that emphasises that $y$ is a variable that depends on $t$ and so is perfectly acceptable. Aug4 revised Computing the sum of an infinite series The sum is not the same as the series itself Aug4 suggested approved edit on Computing the sum of an infinite series Jul29 answered Examples of “Non-Logical Theorems” Proven by Logic Jul24 comment Can universal instantiation be used more than once? If technique X can only be used once in a proof, and I use it to prove A implies B, and use it to prove B implies C, then I wouldn't be able to combine these proofs to show A implies C as that would require two uses, and mathematics would pretty well come to a halt. Jul20 awarded Yearling Jul14 comment Why is the height of a heap defined as $\lg n$? See mathworld.wolfram.com/Lg.html for some discussion of what the notation $\mathop{lg}$ (as opposed to $\log$ or $\ln$) means. Jul14 comment Are the real numbers really uncountable? I'm not sure what the issue is @frogeyedpeas . When a mathematician says "there exists an x such that..." they're not saying "there exists an x, with definition Y, such that...". If you want to, you can study numbers with this property but that has no bearing on the existence of the other numbers. Jul14 awarded Nice Answer Jul14 answered Are the real numbers really uncountable? Jul9 comment How do I know if I have imaginary numbers when using Newton Raphson Method? I guess you're wondering what happens if you're trying to solve an equation that contains complex values, or from a complex starting point. The answer is that it gets complicated. Seriously complicated: chiark.greenend.org.uk/~sgtatham/newton Jul7 comment Integral of the square of a function The integral can easily be non-negative even if the integrand is sometimes not real. Consider a function $f$ that takes a small imaginary value for a small region and otherwise takes large real values. Overall the real parts will dominate the integral giving a non-negative result. Jul6 answered Is $\infty = \frac{1}{0}$? Jul5 comment Axiom of Choice and finite sets "How do I choose such an x?" is often a good question if you're writing a computer program. But in mathematics, if you want to use the existence of $x$ then tautologically you need only a proof that $x$ exists. Jul5 awarded Nice Answer Jul5 revised Understanding matrices. added 202 characters in body Jul4 answered Understanding matrices. Jul4 comment Understanding matrices. That code isn't right. Maybe you mean newX = cos(angle)*oldX-.... Jul4 revised What is the geometric meaning of this integral? added 2 characters in body