# Tagged Questions

For questions concerning a specific proof, asking for verification, identifying errors, suggestions for improvement, etc.

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### Increasing sequence and subsequence

I want to prove this statement, If $x_n$ is an increasing sequence and if some subsequence of it converges, then $x_n$ also converges. My proof is that suppose $x_{n(k)}$ is the subsequence that ...
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### Is it possible for two triangles to be different if the sides of one is equal to another?

I was reading Euclid's Elements E-book I found online and got stuck on this concept. I will just copy what I found to be very absurd. There could still be another different triangle with the same ...
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### Tietze Extension Theorem - How does the induction work?

I am reading a version of the Tietze Extension Theorem here: https://proofwiki.org/wiki/Tietze_Extension_Theorem There was a Lemma that says: And then it was repeatedly applied: How was the ...
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### Alternative proof: show that any metrizable space $X$ is normal - Part 2

This is a follow up to one of my earlier questions I am reading some stuff online and saw a proof as follows Per a comment in Part 1 in linked, We know that $d(C_1,C_2)$ could easily be zero ...
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### $\text{ Proving }\; A \subseteq \Bbb R \text{ A is bounded above} \Rightarrow A^c \text{ is not?}$
Prove: Let $A \subseteq \Bbb R$. Prove that if $A$ is bounded above, then $A^c$, the complement of $A$ is not bounded above. $A^c =$ those element of the universe that are not in A. $\Bbb R =$ ...