Reputation
Top tag
Next privilege 250 Rep.
View close votes
Badges
3
Newest
 Teacher
Impact
~484 people reached

  • 0 posts edited
  • 0 helpful flags
  • 31 votes cast
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.
Mar
23
comment Something that isn't continuous can be proven to be continuous (so it is continuous - definitions - but doesn't look it!)
@Peter: In general, a function is continuous iff the preimage of every open set is open. In the sense of taking the open sets as unions of open intervals around the points (which is implied in the $\epsilon-\delta$ def.), all singletons $\{n\}$ are open--and so all subsets of $\mathbb{N}$ are open. This is an example of a discrete topology, and every function from a discrete topological space to any other topological space is continuous. If the topology on $\mathbb{N}$ is taken to be something else, not all functions from it will be continuous.
Feb
6
comment Is it faster to count to the infinite going one by one or two by two?
@EvgeniSergeev: Not in $\mathrm{ZF}$ set theory, but with some additional axiom, such as axiom of countable choice ($\mathrm{AC}_\omega$), you can. ETA: You can check the wikipedia page on the Dedekind infinite for some details.