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Jan
23
answered Closure of $A \subset \mathbb{R}$
Jan
23
comment Closure of $A \subset \mathbb{R}$
To show that two sets $A,B$ are equal you have to show $A \subset B$ and $B \subset A$ respectively.
Jan
23
revised Closure of $A \subset \mathbb{R}$
edited tags; edited title
Jan
22
revised Find combinations of two digits
Tags edited.
Jan
21
comment Proving if $A$ is a null set and $B$ is a countable set then $A+B$ is null
@LHS That's very kind of you, thank you. Glad I could help. : )
Jan
21
revised Proving if $A$ is a null set and $B$ is a countable set then $A+B$ is null
added 11 characters in body
Jan
21
answered Proving if $A$ is a null set and $B$ is a countable set then $A+B$ is null
Jan
21
comment Conceptualizing Inclusion Map from Figure Eight to Torus
@Pierre-YvesGaillard: Better? : )
Jan
19
revised $B$ an open unit ball in $\mathbb{R}^n$. I need to find a continuous bijective function $f: B \to \mathbb{R}^n$ such that $f^{-1}$ is also continuous
edited title
Jan
17
comment Uncountability of countable ordinals
Ah, I didn't know what downwards closed means. Thanks, Asaf!
Jan
17
comment Uncountability of countable ordinals
I'm confused by the fact: is $\{ \{ \emptyset \} \}$ not downwards closed? Meaning it has a least element with respect to $\in$, or what does downwards closed mean?
Jan
17
comment Injection from the set of countable ordinals $\Omega$ into $\mathbb{R}$
Why is it possible that no injection exists in the absence of choice?
Jan
16
comment Injection from the set of countable ordinals $\Omega$ into $\mathbb{R}$
Thank you! Now I'm trying to figure out in which part of the definition of $f$ I went wrong. The comment in the notes I linked to seems misleading given your answer since it asks to construct $f$ using transfinite induction.
Jan
16
asked Injection from the set of countable ordinals $\Omega$ into $\mathbb{R}$
Jan
16
comment Cardinality of Borel sigma algebra
When is induction done over all ordinals and when over countable ordinals only?
Jan
16
comment (Graphics Gems IV, Shoemake) From matrix to euler angles explanation
What are XEDS angles?
Jan
16
revised Convergence of the next series
"s" added in title.
Jan
16
accepted Characterisation of compact subsets of Banach spaces
Jan
16
comment How to prove that every infinite cardinal is equal to $\omega_\alpha$ for some $\alpha$?
@AsafKaragila I should've read the editing history! Thanks for the comment, Asaf.
Jan
16
comment How to prove that every infinite cardinal is equal to $\omega_\alpha$ for some $\alpha$?
@AsafKaragila Where did you use AC in you answer?