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Apr
8
comment Is “$a + 0i$” in every way equal to just “$a$”?
@Farnight In that different context, I agree with you, but no +1 because I disagree with your first sentence in the original context, effectively agreeing with your second sentence :-)
Mar
13
comment Is there such a thing as proof by example (not counter example)
Good answer to the wrong question (IMHO). This should be at Examples of apparent patterns that eventually fail, if it's not mentioned already.
Mar
10
comment Existence of an holomorphic function
Would a proof by contradiction be "easier", i.e. you want $ \forall f \exists \psi \forall z: \psi(z+1)=\psi(z)+f(z)$ so attempt $ \exists f \forall \psi \exists z: f(z)\neq\psi(z+1)-\psi(z)$. In fact, my first question would be is $\psi(z+1)-\psi(z)$ always holomorphic?
Mar
3
comment Why are 1 and -1 eigenvalues of this matrix?
You do mean the lower right corner of $\mathbf{N}\text{ is }\mathbf{P}^{-1}\begin{bmatrix}1 & && \\ & \ddots && \\ & & 1& \\ &&& -1 \end{bmatrix}\mathbf{P}=\mathbf{P}^{-1}(\mathbf{I}-\begin{bmatrix}0 & && \\ & \ddots && \\ & & 0& \\ &&& 2 \end{bmatrix})\mathbf{P}=\mathbf{I}-2\mathbf{P}^{-1}\begin{bmatrix}0 & && \\ & \ddots && \\ & & 0& \\ &&& 1 \end{bmatrix}\mathbf{P}$?
Mar
3
comment Exotic bijection from $\mathbb R$ to $\mathbb R$
To cover the domain/range of $\pm(0,1)$, I assume $-\infty<k<+\infty$.
Mar
3
comment Inequality from Chapter 5 of the book *How to Think Like a Mathematician*
Can these simpler approaches to a specific example be used to produce a simpler answer to the "general case"?
Feb
24
comment Most ambiguous and inconsistent phrases and notations in maths
Note that even when you correct it, the most remarkable thing is still true: $i^i\in\mathbb{R}$.
Jan
5
awarded  Nice Answer
Jan
2
comment Great contributions to mathematics by older mathematicians
I know this is closed, but I think we've missed an important one: Erdős.
Dec
30
comment What parts of a pure mathematics undergraduate curriculum have been discovered since 1964?
There's 230 years difference there.
Dec
20
awarded  Constituent
Dec
8
awarded  Caucus
Dec
2
revised Are the values generated by non-linear equations truly random?
latex; wikilink
Nov
18
comment How many $\mathbb R$s must a Mathematician walk down?
I haven't confirmed the details but isn't this the solution: Step 1 needs to be a walk in any direction long enough to avoid rounding errors. Step 2 can then be towards one of the possible origins determined by the triangle implied by the two lengths towards it we now have. Step 3 (if needed) is to turn around and walk toward the correct origin if the wrong one was chosen before. (And you now have three lengths pointing to it.)
Oct
28
comment Ratio of product from one point and minimum distance
The simple answer is $1$ (unless any two of the points are coincident, in which case the $m=0$ and the ratio does not exist) but I can see there's probably a better solution because for $n>6,m$ is likely $<|A_0A_k|$.
Oct
20
revised How to prove that $\frac{(5m)!(5n)!}{(m!)(n!)(3m+n)!(3n+m)!}$ is a natural number?
Slightly further...
Sep
30
comment Why is Banach–Tarski's paradox so interesting?
If you mapped only the irrationals $x\in[0,1]\to x+1$, under certain measures you'd have a mapping from $[0,1] \to [0,2)$, at least, but that's definitely not a finite number of sets.
Sep
14
awarded  Electorate
Sep
14
revised Is “$a + 0i$” in every way equal to just “$a$”?
Someone would have pointed it out by now
Sep
9
answered How to read this in English?