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Oct
8
comment The “Empty Tuple” or “0-Tuple”: Its Definition and Properties
@Mathemanic: The Wikipedia definition mirrors the way lists are defined in Lisp (or, more generally, in functional languages). Also, it allows to distinguish e.g. the triple $(a,b,c)$ from both the tuple $((a,b),c)$ and the tuple $(a,(b,c))$.
Oct
8
comment The “Empty Tuple” or “0-Tuple”: Its Definition and Properties
A quite obvious definition of tuples I cannot find on the Wikipedia page: $()=\emptyset$, $(a)=\{\{a\}\}$, $(a,b)=\{\{a\},\{a,b\}\}$, $(a,b,c)=\{\{a\},\{a,b\},\{a,b,c\}\}$, …
Oct
8
comment How is greater than defined for real numbers?
Well, transitivity holds only if the sum of any two squares is again a square; the rational numbers fail this property. Antisymmetry holds only if $x^2+y^2=0$ implies $x=0$ and $y=0$; the complex numbers fail this property.
Oct
8
comment How is greater than defined for real numbers?
@AsafKaragila: It works for $\mathbb C$, it just doesn't give anything useful there (especially no order relation).
Oct
8
answered How is greater than defined for real numbers?
Oct
6
comment Unitary and Self-adjoint complex operator .
Err ... with $v=x+y$, $U(v)=x+y$ means $U(v)=v$; given that this decomposition is possible for all vectors, $U$ is clearly the identity, which is both unitary and self-adjoint. But somehow I think that is not the problem you meant ...
Oct
5
accepted Is the limit of the dual spaces the dual space of the limit?
Oct
5
comment Is the limit of the dual spaces the dual space of the limit?
Very nice. As far as I can tell, your argumentation is correct.
Oct
5
comment A property of homogeneous of degree p functions:
No, you haven't. Note that you're actually calculating the $n$-th derivative only in the first equation (where there's only a polynomial in $t$). In the second equation, you just use $d/dt = \sum dy/dt \partial/\partial y$ repeatedly, and don't try to calculate anything. (note $(d/dt)^n f = d/dt (d/dt)^{n-1} f$; now $(d/dt)^{n-1} f$ is a function, just like $f$ is; note that $f$ itself is left alone, and only $d/dt$ is rewritten in the second equation)
Oct
5
answered A property of homogeneous of degree p functions:
Oct
4
answered x / 3 + y /3 + z / 3 = (x + y + z) / 3?
Oct
4
revised Is the limit of the dual spaces the dual space of the limit?
Added clarification that I mean the algebraic dual space
Oct
4
comment Is the limit of the dual spaces the dual space of the limit?
@Ian: Thanks, I indeed meant the algebraic dual space. I'll add a note to this effect. Of course, the situation with continuous duals might also be interesting.
Oct
4
comment Probability of bit revelaed
I'd say that depends on the probability of the other bits to be 1.
Oct
4
asked Is the limit of the dual spaces the dual space of the limit?
Oct
4
answered In QR decomposition why is $(R^TR)^{-1}R^T = R^{-1}$
Sep
30
awarded  Explainer
Sep
15
comment Combinatorics (Yahtzee)
A large straight is "2-3-4-5-6". But it does not matter which of the dice is 2, which is 3, which is 4, and so on. It just matters that each of those numbers appears. The same is true for all others. In no single case does the score depend on the order.
Sep
15
comment Why is the expression $\underbrace{n\cdot n\cdot \ldots n}_{k \text{ times}}$ bad?
With the underbrace notation, it's not at all clear what $n^0$ is.
Sep
14
revised Write the Fourier series to $f(t)=|\sin t|$
Improved math formatting