Take the 2-minute tour ×  I have this function which approaches
zero in discrete steps:   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?  share|improve this question What do you mean by
"have an asymptote"? –  Antonio Vargas Mar 19 '12 at 2:15 What
is the definition of asymptote you are using? In the ones I
know, continuity is not involved. –  Arturo Magidin Mar 19 '12
at 2:15 Is that supposed to be ${1\over2^{int(x)}}$? If so, can
you edit? –  Gerry Myerson Mar 19 '12 at 2:27 Is this about Big-
Oh notation huh? –  FiniteA Mar 19 '12 at 3:51 @GerryMyerson
Fixed, sorry! –  Charlie Somerville Mar 19 '12 at 7:29 add
comment  1 Answer  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 $y=0$.  share|improve this
ans