Stan Liou
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 Dec 17 comment If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$) @EwanMellor Your version would slightly more clearly be using the given assumption, but since $A\cap B \subseteq A \cup B$ is straightforward, using the equals sign is fine too. Aug 31 comment Why do both sine and cosine exist? @columbus8myhw if on the unit circle, you draw the vertical line tangent to it at $(1,0)$, then take its intersection with angle ray (the other along the positive $x$-axis) then... (1) the height above the x-axis is the tangent of the angle, while (2) the length segment that cuts across the circle along the ray to the vertical line is the secant of the angle. Well, it might not satisfy you as an optimal naming convention, but that's why it was defined that way. Aug 19 comment Why do we not have to prove definitions? @user21820 It's worth noting that Carroll was probably intentionally satirizing modern mathematics, and here the kind of mathematical stance Blass's answer describes, At least, there are many interesting parallels between Wonderland and new-fangled ideas (during Carroll's time), e.g., the Mad Hatter representing Hamilton, and the members of his endless rotary tea party being quaternion units. Jul 9 comment Can math be subjective? Pedantry: the continuum hypothesis would not be "subjective" under ZFC. (But I guess that was just a typo.) May 4 comment Inequality in Algebra: $1 \leq x_1 x_2 \cdots x_n$ implies that $2^{n} \leq (1 + x_1)(1+x_2) \cdots (1 + x_n).$ @wythagoras yes, although you can also think of it as just $(\sqrt{x_i}-1)^2\geq 0$. Mar 6 comment What is an odd prime? @MikeMiller Avoiding anthropocentrism is a laudable goal. ;) Jan 23 comment I can't remember a fallacious proof involving integrals and trigonometric identities. One I learned in calculus class was basically exactly this, except on $\cot x\,\mathrm{d}x = (\sin x)^{-1}\,\mathrm{d}(\sin x)$, so it technically used trigonometry, but was otherwise exactly your answer. Jan 23 comment Soft question: Union of infinitely many closed sets @user192680 the closed intervals don't form a topological basis because they're not open, but you may be interested in a related notion of $F_\sigma$ sets. Jan 23 awarded Teacher Jan 23 comment Soft question: Union of infinitely many closed sets Not any whatsoever, but any in a $T_1$ space. Jan 23 comment Soft question: Union of infinitely many closed sets @DanielMcLaury ok thanks, though the straightforward interpretation would be the empty set. ;) Jan 23 answered Soft question: Union of infinitely many closed sets Jan 22 comment Proving the sum of squares of sine and cosine using the Cauchy product formula +1 for masochism Jan 21 comment What is the proper notation for a general number of nested summations? But the OP's summations are equivalent to sum of ordered tuples, not unordered tuples, so in this case $S$ could be $\{(k_1,\ldots,k_n)\}$. Jan 13 comment If square root is the inverse function of $5^2$ what is the inverse function of $5^1$ You mean $x^n\leftrightarrow x^{1/n}$? That's how roots work. Oct 12 comment Can the distance between two points equals zero 'Physical' distance? Jul 31 suggested rejected edit on Produce unique number given two integers Jul 1 awarded Commentator Jul 1 comment Meaning of math symbol ~ Thinking on it, though the notation is seems somewhat unusual in this context (at least in my experience; ymmv), it actually makes more sense. Limits are defined on functions, so something like $\lim\frac{f(n)}{g(n)}$ only makes sense by implicitly interpreting it as the limit of another function that's defined by pointwise division. Thus, one might as well make it explicit and write $\lim\left(\frac{f}{g}\right)(n)$. Jul 1 comment Meaning of math symbol ~ @JamesWood: the notation is standard in the sense widely understood, but unusual in the sense that it would not be typically used in this context. All $(f/g)$ means is the function defined pointwise by that ratio.