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  • 35 votes cast
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.
Jun
23
comment Derivative in calculus $f(t)= 7\sinh(\ln t)$
Why not just distribute the division by $t$ before differentiating?
Jun
3
comment Why do negative exponents work the way they do?
Is the question about why $x^{-a} = 1/x^{a}$ is mathematically valid or about why so many algebra/precalculus classes insist that students always re-write all the exponents to be positive?
May
23
comment Algebra: What allows us to do the same thing to both sides of an equation?
@matth: injective means $f(a)=f(b)\Rightarrow a=b$ for all $a,b$. Since $(a)^2 = (-a)^2$, the squaring function is not injective. Graphically, injective function "pass the horizontal line test", i.e. no horizontal line intersects the graph more than once.