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2answers
443 views
+50

Ratios in big-O notation?

Hi can anyone give me a counter example of the following claim: f(n) = O(s(n)) and g(n)=O(r(n)) imply f(n)/g(n) = O(s(n)/r(n)) Thank you
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4answers
98 views
+50

Prove that the vectors $v_1,v_2,\ldots,v_k \operatorname{span}R^n$ if and only if $[v_1]_B,[v_2]_B,\ldots,[v_k]_B \operatorname{span}R^n$.

From section on Change of Basis $\longrightarrow$ Assume the vectors $v_1,v_2,\ldots,v_k\operatorname{span}R^n$, we must show that $[v_1]_B,[v_2]_B,\ldots,[v_k]_B\operatorname{span}R^n$. We can ...
1
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3answers
58 views
+100

Show that if the projection of a set is negligible, then the set is negligible as well

I'd like a hint in the right direction, im drawing a complete blank. let $E \subset \mathbb R^2$. We'll define the projection of $E$ unto the $x$ axis as: $P_x(E)=\{x| \exists y \in \mathbb R s.t ...
2
votes
0answers
71 views
+50

3-Coloring a graph using propositional formulas

Hello everyone I am studying for an exam on logic and computability, I am trying to tackle a specific problem so any help would be greatly appreciated: Let $G = (V,E)$ be an undirected graph ...
1
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0answers
48 views
+50

Is the complement of the inversion relation (in the context of permutations) transitive?

I'm studying from An Invitation to Discrete Mathematics where I came upon an exercise which confuses me. Let $\pi$ be a permutation of the set $\{1,2,\dots,n\}$ and let $I(\pi)$ denote the set of ...