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Apr
30
revised Inclusion of representations: $\pi_1(A)^{''}\subseteq \pi_2(A)^{''} \Rightarrow \pi_1(A)\subseteq \pi_2(A)$?
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Apr
29
answered Inclusion of representations: $\pi_1(A)^{''}\subseteq \pi_2(A)^{''} \Rightarrow \pi_1(A)\subseteq \pi_2(A)$?
Apr
29
comment Why is $n^0 = 1$?
That is one point of view, but not the only one. You can start with ZFC and use the axioms to construct the naturals as the minimal set satisfying the axiom of infinity; in that case $0$ is defined as the empty set, and it is an original member of $\omega$.
Apr
29
comment Why is $n^0 = 1$?
It depends on how you define the natural numbers and their addition. But usually yes, you define $0$ as the number that satisfies $0+n=n$ (if you are adjoining $0$ to the monoid), or you define addition by zero by $0+n=n$, if you are defining addition recursively from the Peano axioms: in both cases it is a convention, inspired by the notion of "adding nothing".
Apr
29
comment Why is $n^0 = 1$?
I don't "dismiss it as a convention": I think that it is a great convention, and I agree (and I imply it in my answer) that the reason for the convention is algebraic.
Apr
29
comment Why is $n^0 = 1$?
Of course it is a convention. Algebraic structures don't know about notation.
Apr
29
answered Why is $n^0 = 1$?
Apr
29
comment What is wrong with this limit reasoning
@mookid: it is not true that $o(1)\to0$. What happens there is that $x-\sin x=o(x^3)$.
Apr
29
answered Operator norm and L infinity norm
Apr
29
answered Improper integral test
Apr
29
answered weak convergence lim inf sequence example
Apr
29
answered Difference between open sets and open balls in metric space
Apr
29
comment weak convergence lim inf sequence example
In your title you talk about weak convergence, but in the question you seem to be talking about sequences of numbers? What is the question about?
Apr
28
answered Spectral measure associated to eigenvector of self-adjoint operator
Apr
28
answered weak-star convergence to Dirac Delta function
Apr
28
answered question about a proof on Murphy's book about $C^*$-algebras
Apr
28
answered An extension of a corollary to Fuglede's theorem
Apr
28
answered $\ker f$ is either dense or closed when $f$ is a linear functional on a normed linear space
Apr
27
comment Strictly positive element in a C*-algebra
No, it does not mean that. It means, as it says, " the hereditary C$^*$-algebra generated by $a$".
Apr
27
revised Strictly positive element in a C*-algebra
edited tags