I am trying to find the infimum and supremum of the following sets, however I can't check if my answers are correct. The sets are:

$$\begin{aligned} &a)\,S=\{x\big|x=-(1/n)+[1+(-1)^n]n^2,n\geq1\}\\&\implies \sup S=\infty,\,\inf S=-1\\ \\ &b)\, S = \{x\in\mathbb{Q}\big|x^2<2\}\\&\implies \sup S=\sqrt2,\,\inf S=-\sqrt2\\ \\ &c)\,S=\{x\big| |2x+1|<5\}\\&\implies \sup S=2,\,\inf S=-3\\ \\ &e)\,S=\{x\big|(x^2+1)^{-1}>1/2\}\\&\implies \sup S=1,\,\inf S=-1 \end{aligned}$$ Would these results be correct?


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