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 Sep16 comment limit inferior and superior for sets vs real numbers Thanks Arturo for the very elaborate explanation. I think I understand the concepts now. Sep16 comment limit inferior and superior for sets vs real numbers For $B_n={1/n}$, shouldn't the $lim~inf~B_n$ and $lim~sup~B_n$ be $\{ 0 \}$ because $lim sup(1/n)=0$ and $lim inf(1/n)=0$ ? Sep16 comment limit inferior and superior for sets vs real numbers never mind got it. I realize that A_n represents a sequence of sets. Sep16 comment limit inferior and superior for sets vs real numbers very nice examples. I didn't understand the 2) example. How did the lim inf get inside the indicator function? Shouldn't limsup and liminf of an indicator function always be 1 and 0, respectively? Sep16 comment limit inferior and superior for sets vs real numbers this example helps make things much clearer. thanks! Sep16 accepted limit inferior and superior for sets vs real numbers Sep16 revised limit inferior and superior for sets vs real numbers added 35 characters in body Sep16 revised limit inferior and superior for sets vs real numbers added 12 characters in body; deleted 8 characters in body; added 16 characters in body; added 22 characters in body Sep16 comment limit inferior and superior for sets vs real numbers edited to add curly braces correctly. Sep15 awarded Editor Sep15 comment limit inferior and superior for sets vs real numbers I have added some examples. Can you please answer that will help clarify. Sep15 revised limit inferior and superior for sets vs real numbers added 178 characters in body Sep15 asked limit inferior and superior for sets vs real numbers Sep13 awarded Commentator Sep13 comment Pivoting in LU decomposition To summarize, LU decomposition with pivoting does not require matrix to have positive principal minors, it only requires matrix to be non-singular. So it is more stable. The answers below explain what stability means in greater detail. Thanks everyone. Sep13 accepted Pivoting in LU decomposition Sep9 comment if eigenvalues are positive, is the matrix positive definite? @J.M. can you give an example of a positive definite but asymmetric matrix? Sep9 asked if eigenvalues are positive, is the matrix positive definite? Aug31 asked Pivoting in LU decomposition Aug16 comment square root of symmetric matrix and transposition alex - I don't think Q D^{1/2} Q going to be triangular matrix. take for example A = ((2,-2),(-2,5))