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A duck walks into a bar. Animal control is promptly called and the duck is released into a near by park.

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12h
comment Why is this map not surjective at the origin?
@Strants: It's not clear, but I interpreted the OP as "this is a line I read somewhere" ... "why is it so?". In any case, I guess he knows that the codomain isn't just $\{0\}$, so pointing out that the function is constant should tell that it's not surjective.
12h
answered Why is this map not surjective at the origin?
2d
reviewed Approve Is $g$ the unique function with this property?
2d
answered Is $g$ the unique function with this property?
2d
comment Have any definitions in mathematics been redefined
I'd maybe formulate the question as asking for historical re-definitions of word usage. The idea that "the primes (as such) have be re-defined to not include 1" feels weird. You just defined a new mathematical entity but didn't give it a new name. Also, in a way things like sets are indirectly defined differently with each new set theory.
Dec
15
comment What does not having a first-order frame imply for models?
Is this answer about the models for sentences such as the McKinsey formula? I don't quite understand.
Dec
15
asked What does not having a first-order frame imply for models?
Dec
12
comment What makes a limit 'go away'?
I guess I like this, but it's probably more clear if you first make the substitution $\mathrm{e}^{-x}\Rightarrow\frac{1}{\mathrm{e}^{x}}$ instead of rewriting $-(+\infty)\Rightarrow-\infty$.
Dec
12
comment The Order of Mixed Quantifiers
cstheory.stackexchange.com/questions/4473/…
Dec
11
comment “Novel” proofs of “old” calculus theorems
Constructive math is cautious about it's tools and reproves many theorems. Also, some theorems don't go through (as viewed form the constructive perspective) and are substituted by variations, e.g. this. The are improvement in that they actually contain algorithms for forming this and that object. See also this talk. It also reminds me of Reverse mathematics.
Dec
11
comment “Novel” proofs of “old” calculus theorems
Do proofs avoiding assumption of certain postulates, like excluded middle, count as improvement to you? If so, there are surely many of those not usually provided in textbooks.
Dec
11
comment There is no smallest infinity in calculus?
@Oria: I like your way of thinking.
Dec
11
revised What is the Fourier transform of $\frac{x}{\sin(x)}$?
added 48 characters in body; edited title
Dec
11
comment 1:1 between N and P(N)
The question has been answered I guess, but could you make more clear how your assignment looks like. Which number gets mapped to which concretely specified subset? Do you first map from ${\mathbb N}$ to ${\mathbb N}\times{\mathbb N}$ (is this injective?) and then to the power set? Of if not, have you computed which number gets replaced in the initial enumberations of sets of subsets?
Dec
11
comment Is $(-\infty, \infty)$ an interval?
It's a section of the real number line which contains every intervals you could come up with. I think instead of asking if $(\infty,\infty)$ is an interval, you should ask if $(\infty,\infty)$ is usually defined to be an interval. Since it's not obvious to you or me, it is a matter of conventional terminology. More so than, say, to ask if 7 is a natural number - where we break all of the other core conceptions if we negate it.
Dec
10
comment Solve $f\left(\frac{x-3}{x+1}\right)+f\left(\frac{x+3}{x+1}\right)=x$ $\forall x\neq -1$
He starts out with "Given $f(x)$", but I take it he wants any $f$ which has this property.
Dec
8
awarded  Caucus
Dec
7
comment evaluating the indefinite integral of $\int \frac{3x}{x-2}dx$
@Sumo: you beat me by 13 minutes.
Dec
7
comment How to use bijection of two sets to define a bijection of their respective differences?
A question would then be, in general, how to capture equinumerosity of two sets in FOL, without restrictions on A and B, and without introducing ordered pairs.
Dec
7
comment How to use bijection of two sets to define a bijection of their respective differences?
@ZhenLin: Okay, thanks! What I try to find out with this question is actually this: If $B\subseteq A$, does the following predicate capture equinumerosity? $B≈A:=∃f. [to ∧ from]$ where $to = ∀(b ∈ B). ∃!(fb). ∃(p ∈ f). ∀x. [[x ∈ p] ↔ [x = b ∨ x = (fb)]]$ and $from=∀(a ∈ A). (a ∈ B) ∨ ∃((inva) ∈ B). ∃(p ∈ f). ∀x.[[x ∈ p] ↔ [x = (inva) ∨ x = a]]$. At the moment, this is my conclusion from the tedious work of reverse-engineering the Grothendieck-Tarski axioms in terms of primitive FOL symbols here. I didn't find equinumerosity defined anywhere else.