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0 1 $begingroup$ I was trying to understand what definitional expansion mean. Consider having two L-structures $mathcal A$ and $mathcal A'$ where $A'$ is an L'-expansion of $mathcal A$ . We way that $mathcal A'$ is a definitional expansion of $mathcal A$ if for each symbol $s in L' setminus L$ the interpretation of $s^{mathcal A'}$ of $s$ in $mathcal A'$ is 0-definable in $mathcal A$ . I understand what zero definable for a set is, which means: $$ varphi^{mathcal A} = { (a_1,...,a_m) in A^m mid mathcal A models varphi(a_1,...,a_m)}$$ when its zero definable the L-formula $varphi$ is only in terms of $L$ (and not the names of the elements of the underlying set $a in A$ ). However in this context we have a single element. We say its zero definable ok perhaps that means t

0 1 $begingroup$ Determine the following limit, or show it doesn't exist: $$lim_{nto infty}(sinsqrt{n+1} - sinsqrt{n}) .$$ I'm not sure how to proceed. I know that I can't use limit arithmetic because both $lim_{nto infty}sinsqrt{n+1}$ and $lim_{nto infty}sinsqrt{n}$ diverge, although I'm not really sure that fact is all that useful in solving this. calculus limits trigonometry share | cite | improve this question edited Dec 18 '18 at 4:24 tatan 5,797 6 27 60 asked Dec 18 '18 at 4:02