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I have this function which approaches zero in discrete steps:

$\frac{1}{2^{int(x)}}$

My question is that although this function shows asymptotic behaviour in that it approaches $y=0$ does it still have an asymptote even though it isn't continuous?

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    @GerryMyerson Fixed, sorry!2012-03-19

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One usually says that a function $f:(a,\infty)\to\mathbb R$ has horizontal asymptote $y=c$ if $\lim_{x\to \infty} f(x)=c \tag1$ The function $f(x)=2^{-\lfloor x\rfloor }$ satisfies (1) with $c=0$ and therefore has horizontal asymptote $y=0$.