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  • 40 votes cast
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.
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?