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comment Prove the inclusion-exclusion formula
No more subtraction rule. Just rearrangement of the terms.
Apr
23
comment Prove the inclusion-exclusion formula
@Csci319 I'd put your intermediary result as a step before the final one, but that's a matter of taste.
Apr
23
comment Manually plotting some particular graphs
@SanchayanDutta Thanks for checking. I fixed it now.
Apr
23
revised Manually plotting some particular graphs
added 96 characters in body
Apr
23
comment Prove the inclusion-exclusion formula
@Csci319 Not quite. Your term is what the parentheses expand to. The final result will be the given formula, of course.
Apr
23
awarded  Nice Answer
Apr
23
comment Show that every k-dimensional vector subspace V of $R^N$ is a manifold diffeomorphic to $R^k$.
You should look up on linear algebra books ;) They should be in any introductory book. The only differences in the differential-topology setting can be neglected when in finite-dimensional vector spaces, where an atlas (of $V$) can consist of a linear map ($\varphi$ here) and the entire space ($\mathbb R^k$ here).
Apr
23
answered Manually plotting some particular graphs
Apr
23
reviewed Edit Manually plotting some particular graphs
Apr
23
revised Manually plotting some particular graphs
error in tag because this question doesn't belong to graph theory
Apr
23
comment Show that every k-dimensional vector subspace V of $R^N$ is a manifold diffeomorphic to $R^k$.
First of all you can fix $\{e_i\}$ as the canonical basis of $\mathbb R^k$. Then chosing a basis of $V$ as in the text, the representation Matrix of $\varphi^{-1} : \mathbb R^k \to V$ is simply $$[\varphi^{-1}]_{\mathfrak E \to \mathfrak B} = \pmatrix{1&0&\cdots\\0&\ddots&\\\vdots&&1} = I_k$$
Apr
23
comment Prove the inclusion-exclusion formula
@Csci319 Nowhere. It only servers as a start to make the first application of IEP for two sets more obvious.
Apr
23
comment Using these number's logarithm with base 10 compare a with b when knowing $log_3(a)=log_5(b)$.
What do you have in mind? $$a = \log_5(3) \cdot b$$
Apr
23
comment Show that every k-dimensional vector subspace V of $R^N$ is a manifold diffeomorphic to $R^k$.
Can you see that $\varphi$ is a vector space isomorphism between $V$ and $\mathbb R^k$?
Apr
23
comment Prove that range of operator is closed.
The question title is no replacement for the problem statement. I've edited your post to include a more concise title and introduced MathJax to improve readability :)
Apr
23
revised Prove that range of operator is closed.
added 212 characters in body; edited title
Apr
23
answered What is cosine to the power of zero?
Apr
23
revised Sigma-algebra: $\sigma(\mathcal{A})=\mathcal{A}$?
edited tags
Apr
23
comment Sigma-algebra: $\sigma(\mathcal{A})=\mathcal{A}$?
What else should it be? Removing anything from $\mathcal A$ makes it not contain the generator. Adding anything makes it bigger than necessary.
Apr
23
revised How to prove or disprove this algebraic inequality?
rolled back to a previous revision