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Results tagged with solution-verification
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user 663571
For posts looking for feedback or verification of a proposed solution. "Is this proof correct?" is too broad or missing context. Instead, the question must identify precisely which step in the proof is in doubt, and why so. This should not be the only tag for a question, and should not be used to circumvent site policies regarding duplicate questions.
1
vote
Accepted
Prove by induction that $\sum_{i=1}^{k} a^{k-i} b^{i-1}=\frac{a^{k}-b^{k}}{a-b}$
So everything in your proof is correct, but you made a mistake in your first line with indexing. What you actually want to show is $$\sum_{i=1}^{k+1}a^{k+1-i}b^{i-1}=\frac{a^{k+1}-b^{k+1}}{a-b}$$ inst …
- 782
4
votes
1
answer
119
views
Konig's tree lemma without using axiom of dependent choice
Konig's tree lemma says that, if $T$ is a rooted tree such that has infinitely many nodes where each node has a finitely many successors, then $T$ has an infinite branch.
I think I have a proof (which …
- 782
0
votes
1
answer
35
views
Proof Verification: identifying quotient of submodules
Let $M$ be $R$ module, $M_1,M_2,S$ be $R$ submodules of $M$ such that $M_1\subset M_2$.
Let $N_1$ be the $R$ submodule of $M$ generated by $M_1$ and $S$, let $N_2$ be the $R$ submodule of $M$ generate …
- 782
2
votes
1
answer
76
views
Proving that product of two-point sets is compact
I am reading Jech's Axiom of Choice, and I want to prove:
For a non-empty set $I$, if $\{0,1\}^I$, the generalized Cantor space, is non-empty compact, then $\prod_{i\in I}A_i$ where $|A_i|=2$ for all …
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4
votes
0
answers
110
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Prime Ideal Theorem implies Hahn Banach Theorem
I am reading Jech's Axiom of Choice, and there is this exercise: chapter 2 Problem 19:
Show that the Hahn-Banach Theorem follows from the Prime Ideal Theorem.
I came up with a (possibly wrong) proof …
- 782