POV-Ray : Newsgroups : povray.off-topic : Turing determination : Re: Turing determination Server Time
9 Oct 2024 03:55:11 EDT (-0400)
  Re: Turing determination  
From: Darren New
Date: 23 Jul 2009 13:14:29
Message: <4a689a75$1@news.povray.org>
Warp wrote:
> Darren New <dne### [at] sanrrcom> wrote:
>> So if your input isn't unbounded, then O() doesn't make much sense.
> 
>   Of course it makes sense. "How many steps are needed to sort an array
> of 10 elements?"

But O() notation is defined as a function related to an "n" input size that 
grows without bound.

"""
In mathematics, computer science, and related fields, big O notation 
describes the limiting behavior of a function when the argument tends 
towards a particular value or infinity, usually in terms of simpler functions.
"""

http://en.wikipedia.org/wiki/Order_notation

What's the argument that's tending towards infinity?

>   You are basically arguing that "O(1)" doesn't make sense.

No, it makes perfect sense as long as some input value is getting 
progressively larger. (Or heading towards a value that takes progressively 
more time or space.)  O(1) is the *output* when the *input* grows without 
bound. If your input grows without bound, the function isn't meaningful.

-- 
   Darren New, San Diego CA, USA (PST)
   "We'd like you to back-port all the changes in 2.0
    back to version 1.0."
   "We've done that already. We call it 2.0."


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