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AxiomOfChoice

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**An example of a function that attains the value "infinity" on R?**

I'm reading a couple of books on introductory measure theory (Royden, Stein-Shakarchi), and both of them talk about functions that can possibly attain the value [itex]\infty[/itex]. But they don't define exactly what this means, or give examples. So can someone list some examples? Does [itex]1/x[/itex] attain the value of [itex]\infty[/itex] at [itex]x=0[/itex]? Does [itex]1/x^2[/itex]? In this sense, is the latter function continuous at [itex]x=0[/itex], whereas the former isn't?