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Jan
12
comment Difference between complete and closed set
@JonasMeyer Thank you! My confusion arose from the fact that I considered $\sqrt{2}$ a limit point of $\mathbb{Q}$ in $\mathbb{Q}$ I think. And as anon stated concisely. "A limit point of X in Y has to actually exist in Y.".
Jan
12
comment Difference between complete and closed set
@JonasMeyer So when Wikipedia writes "a set is closed if and only if it contains all of its limit points", then this is under the assumption that the space is a complete metric space? I'm asking because then the Wikipedia entry would be wrong.
Jan
12
revised Difference between complete and closed set
Tags edited and typo fixed.
Jan
12
revised Original works of great mathematician Évariste Galois
Accent aigu ajouté.
Jan
12
answered a question on transfinite recursion on $\mathbf{ON}$
Jan
12
comment I want to know why $\omega \neq \omega+1$.
@John Yes, it helped me a lot, too : )
Jan
12
revised I want to know why $\omega \neq \omega+1$.
Latex added.
Jan
12
answered I want to know why $\omega \neq \omega+1$.
Jan
12
comment Converting to partial fractions
I'd like to second that.
Jan
11
comment How to understand the regular cardinal?
According to the examples on Wikipedia the "easiest" example of a regular cardinal are the finite ordinals.
Jan
11
comment Looking for a proof of the completeness of $C^{n}[0,1]$.
@Kyle Glad I could help : )
Jan
10
comment Looking for a proof of the completeness of $C^{n}[0,1]$.
@YemonChoi As for your last sentence in your last comment: I second that.
Jan
10
comment Looking for a proof of the completeness of $C^{n}[0,1]$.
@YemonChoi Yes, that's the uniform limit theorem. : )
Jan
10
comment Looking for a proof of the completeness of $C^{n}[0,1]$.
@YemonChoi The OP was not about $C^1([0,1])$ so this is not a "full" solution. As for general practice: I think a full solution is more helpful than a one liner pretending to be a hint. : )
Jan
10
comment Looking for a proof of the completeness of $C^{n}[0,1]$.
@YemonChoi The $n$-th derivative is continuous and bounded. Where would you use uniform continuity in the proof?
Jan
10
revised Pointwise convergence of a function
added 8 characters in body
Jan
10
revised Looking for a proof of the completeness of $C^{n}[0,1]$.
added 137 characters in body
Jan
10
answered Looking for a proof of the completeness of $C^{n}[0,1]$.
Jan
9
revised Characterisation of compact subsets of Banach spaces
deleted 30 characters in body
Jan
9
revised Characterisation of compact subsets of Banach spaces
deleted 62 characters in body