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on reading ``o(1)''

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Suppose f in o(1).  By definition, there's a natural number n(0) such
that for any c > 0

  0 <= f < c * 1 = c

for any n >= n(0).  (AFAIK, c is a real number.)  That seems to imply
that f = 0 because that's the only thing that could be less than any 
c > 0. 

So I thought saying f in o(1) would be useless, but searching for its
use I see mathematicians writing it out in apparently meaningful ways.

As for example in ``[t]he most obvious method to find small prime
divisors of n is trial division: divide n by 2, 3, 5, etc.  This takes
time y^{1 + o(1)} if n has y^o(1) bits.''[1]

I don't believe he meant ``if n has y^0 bits''.  So how should I 
read ``o(1)''?

Thank you.

[1] How to find small factors of integers.  D.J. Bernstein, 2002.
URL: https://cr.yp.to/papers/sf.pdf

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on reading ``o(1)'' Daniel Bastos <dbastos@toledo.com> - 2017-03-24 21:29 -0300
  Re: on reading ``o(1)'' Kaz Kylheku <336-986-7787@kylheku.com> - 2017-03-25 02:40 +0000
  Re: on reading ``o(1)'' Michael Forsythe <forsythe@example.com> - 2017-03-25 05:51 +0000
    Re: on reading ``o(1)'' Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-03-26 22:14 +0100
      Re: on reading ``o(1)'' Michael Forsythe <forsythe@example.com> - 2017-03-28 10:32 +0000
      Re: on reading ``o(1)'' Michael Forsythe <forsythe@example.com> - 2017-03-28 10:33 +0000
  Re: on reading ``o(1)'' Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-03-26 22:11 +0100
    Re: on reading ``o(1)'' Daniel Bastos <dbastos@toledo.com> - 2017-03-28 21:05 -0300
      Re: on reading ``o(1)'' Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-03-29 14:23 +0100
        Re: on reading ``o(1)'' Daniel Bastos <dbastos@toledo.com> - 2017-04-03 09:40 -0300

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