Matrix algebra : matrix nilpotent
$\operatorname{tr}(A)=\operatorname{tr}(A^{2})= \ldots = \operatorname{tr}(A^{n})=0$ implies $A$ is nilpotent
How do I read the manifest file for a webapp running in apache tomcat? Best way to strip punctuation from a string It seems like there should be a simpler way than:  import string s = "string. With. Punctuation?" # Sample string  out = s.translate(string.maketrans("",""), string.punctuation)   Is there? Check if a class is derived from a generic class How do I resolve "WILL_NOT_PERFORM" MS AD reply when trying to change password in scala w/ the unboundid LDAP SDK? Differential Geometry-Wedge product How can we prove the following relation for differentiating the wedge product of a p-form $\alpha_p$ and a q-form $\beta_q$$$d(\alpha_p\wedge\beta _q)=d\alpha_p\wedge\beta_q+(-1)^{p}\alpha_p\wedge d\beta_q$$ When to pull loose teeth My 5 year old is starting to have some teeth become loose. Specifically her lower two front teeth. I just noticed today that one of them is really loose. However, I don't know how loose it should be before pulling it out.  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A function for which one-sided limits are zero and infinity Natural deduction, Proof $\vdash$ $P\Rightarrow(Q\Rightarrow P)$ So I have a question regarding natural deduction, are we allowed to "copy" our previous assumption inside a new assumption. I will use an example to illustrate.  $\vdash$ $P\Rightarrow(Q\Rightarrow P)$  So here are my steps.  1.) $P$             Assumption  2.)$Q$             Assumption  3.)$P$             Copy (1)  4.)$Q \Rightarrow P$   Implication Introduction  5.)$P \Rightarrow (Q \Rightarrow P)$ Implication Introduction  Is my proof correct, or is there something missing. Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$ How would I go about proving that  $$|a|+|b| \leq |a+b|+|a-b|$$  Using the triangle inequality?  I tried squaring both sides, yielding:  $$|a|^2 +|b|^2 +2|a||b| \leq 2|a|^2+2|b|^2+2||a|^2-|b|^2|$$  Is it correct to move the terms to the other side? 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