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Dec
31
comment Clarifying the definition of “unstable”
@J.M. Hmmm. I just re-read the question and it reads to me as "Are there any algorithms where the error of the algorithm is insignificant with respect to the method itself?" But the algorithm is the method itself. Am I confused?
Dec
31
comment Clarifying the definition of “unstable”
@J.M. True, I forgot about ill-conditioned problems. But I've not heard of forward and backward stability I think. Yet I don't think this falsifies my answer.
Dec
31
comment Set Notation Excercise
Yes, exactly : )
Dec
31
answered Set Notation Excercise
Dec
31
answered Clarifying the definition of “unstable”
Dec
31
revised Relative homology groups of the torus
edited title
Dec
31
answered Relative homology groups of the torus
Dec
30
comment Showing that this is a group under matrix multiplication
@John Yes, it's what you have to show. The second line above shows exactly that. : )
Dec
30
comment LIM is cofinal in ON
: ) But that's what I wanted to show!
Dec
30
comment LIM is cofinal in ON
I think I have figured it out now: Assume $M$ is a cofinal subset of ON. Then for every $\alpha$ in ON there is a $\beta$ in $M$ such that $\alpha \leq \beta$. Then consider $\bigcup M + 1$. This is an ordinal. But there is no $m \in M$ such that $\bigcup M + 1 \leq m$, therefore $M$ cannot be a set.
Dec
30
comment LIM is cofinal in ON
Where do you use cofinality in the first part of your proof?
Dec
30
comment LIM is cofinal in ON
I was quite confused yesterday. Now I think that in your first comment the second part is superfluous. To show that a cofinal subclass is proper it's enough to assume that it's a set and produce a contradiction.
Dec
30
comment LIM is cofinal in ON
I thought the von Neumann universe was the universe of all sets. So it's bigger than ON.
Dec
30
comment LIM is cofinal in ON
Can this proof be modified into not using the von Neumann universe?
Dec
29
comment LIM is cofinal in ON
Thank you, Asaf.
Dec
29
comment LIM is cofinal in ON
Is showing that every cofinal class of ON is proper also a one liner?
Dec
29
accepted Swapping a limit and a $\sup$
Dec
29
accepted LIM is cofinal in ON
Dec
29
asked LIM is cofinal in ON
Dec
29
comment How to evaluate $\int_{1}^{2}\frac{dx}{1+x+\ln x}$?
wolframalpha.com/input/…