Re: on reading ``o(1)''

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From	Ben Bacarisse <ben.usenet@bsb.me.uk>
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Subject	Re: on reading ``o(1)''
Date	Sun, 26 Mar 2017 22:14:49 +0100
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Michael Forsythe <forsythe@example.com> writes:

> Daniel Bastos <dbastos@toledo.com> wrote:
>> 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. 
>
> I believe there are two problems.  The first is that you are writing
> `o(1)', but the paper is using `O(1)'. The two are rather different,
> and I think you want to be talking about O(1).

The paper appears to use both, and the OP's quote from the paper has
what appears to be a very clear small o (and the paper is littered with
them).

> The second is that your definition seems to have misplaced a
> quantifier.

Not if, as I think is the case, the OP meant to define little-o(1).

<snip>
-- 
Ben.

Thread

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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