Oh, Terese, I want to be pedantical. The use of oscillate in your citation refers not to a function or sequence’s endless & effortless extension (tireless because mathematical), but to its behavior while so continuing. Conventionally, that means that its up-and-down y value moves between two limits (as you depict). On the complex plane, a similar sequence would be 0, i, 0, i, … .
If a different sequence were defined after rotating all values exactly 90 degrees [say, by multiplying by the square root if minus one (or “i”)], thereby using the usual vertical axis in place of the usual horizontal axis, one could define a sequence (but not a function), that would oscillate along the vertical between zero and a generalized horizontal value: 0, x, 0, x, 0, x … .
But I digress.
Allen
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