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Jan
27
comment Difference between $\mathop{\text{div}} \vec x$ and $\vec \nabla \cdot \vec x$?
@queueoverflow On page 44 of the following german text (essentially the last page), there are given some examples why $\nabla$ is best thought of as just a notational convenience. However, the gradient ($\operatorname{grad} f=\nabla f$) is a covector.
Jan
25
answered How to realise N-point FFT?
Jan
20
awarded  Informed
Jan
5
comment In a ring homomorphism we always have $f(1)=1$?
@akkkk Universal algebra: "variety"/"quasivariety". Logic/model theory: "model homomorphism", "free model", "set of Horn clauses". OK, I somehow get the impression that I'm unable to convey this information with a single word. I probably have to write a complete answer with full details.
Jan
4
comment Paradox: Any set theory without universe set is not a model of itself
I don't understand the downvote. If I understand you and Zhen Lin correctly, you are claiming that if we could prove that there is a set model in $ZFC$ for itself without assuming $Con(ZFC)$, then we would have proved $ZFC \vdash Con(ZFC)$. This may be true, but it's not obvious to me why.
Jan
3
comment Paradox: Any set theory without universe set is not a model of itself
I learned about this from SEP in the article about alternative set theories, which was written by Randall Holmes. The wikipedia article about pocket set theory cites Rudy Rucker as the inventor of that theory, but everything I have read about it so far was written by Randall Holmes.
Jan
3
asked Paradox: Any set theory without universe set is not a model of itself
Jan
3
accepted Can second order logic express each (computable) infinitary logic sentence?
Jan
3
asked Can second order logic express each (computable) infinitary logic sentence?
Jan
2
revised Calculating volume change of sphere with differential
fixed formula for volume of sphere
Jan
2
suggested approved edit on Calculating volume change of sphere with differential
Jan
2
answered finding $F$ and $G$ for this PDE
Jan
1
comment Order embedding from a poset into a complete lattice
The statement "$\mathcal L$ embeds (as a sublattice) into any complete lattice that contains $\mathcal P$" is false. It only embeds as a partially ordered set.
Dec
20
comment Zeros of Fourier transform of a function in $C[-1,1]$
@ybungalobill Based on the answer to the other question, the proof should now be complete. But since this is homework, I would also be interested to learn about the "official" solution, i.e. a solution which doesn't need to reference some strong or unknown theorem on the way.
Dec
20
revised Zeros of Fourier transform of a function in $C[-1,1]$
ref
Dec
20
accepted Polynomial bounded real part of an entire function
Dec
20
comment Zeros of Fourier transform of a function in $C[-1,1]$
@ybungalobill I asked the missing part as a separate question. The Cauchy-Riemann equations are the reason why I believe that there can't be an essential singularity. However, the ... was more meant to symbolize a laborious cornering of the function instead of an elegant argument. I'm curious whether somebody will present an elegant argument.
Dec
19
asked Polynomial bounded real part of an entire function
Dec
19
answered Zeros of Fourier transform of a function in $C[-1,1]$
Dec
17
comment Induction versus Natural Numbers
An infinite number is one which is not finite in the intuitive sense. As you describe, a number is finite in the intuitive sense, if it can be arrived at by "adding ones finitely many times". Anyway, I slightly changed my mind about these issues, because I learned that first-order logic can define the set of non-standard natural numbers. It's only unable to define the negation of this property.