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Kevin Wampler wrote:
> inputs I'm actually having trouble thinking of a case where this is true
I don't know what "this" you're talking about. Your comments don't make
sense in the context of the bit you quoted.
> My example with big-O notation was actually slightly different than
> that.
Right.
> Thus saying that every program on a finite
> machine finishes in O(1) times is sort of disallowing infinity in one
> area while letting it slip by in another.
Basically, yes.
> My point with big-O notation was instead that the allowance of
> arbitrarily large inputs in the definition is actually massively
> simplifies the problem.
I didn't mean to say it didn't. I thought I had only said it was more
interesting with infinities.
> I'm not entirely sure that we actually have different viewpoints on
> this, and it's possible that I'm just misunderstanding your argument.
> I'm mostly basing my assumptions about your position on your comment:
>
>> Funny enough, infinities make things much more complicated. That's why
>> virtually every bit of math deals with infinities.
>
> Which seems to run counter to my experience,
In many cases where everything is finite, the math becomes trivial, because
math doesn't care how big something is if it's bounded.
I probably should have added an "often" in there. Infinities often make
things more complicated.
> where I'm used to seeing
> unbounded values allowed as a simplifying assumption, and see them as
> common because it's such a powerful tool for allowing general statements
> about whatever branch of math you're considering.
Sure. I didn't mean using infinities in the analysis always makes things
more complicated. I meant using infinities in the problem statement makes
things interestingly complicated, as opposed to problems where everything is
finite, everything halts, etc.
--
Darren New, San Diego CA, USA (PST)
Serving Suggestion:
"Don't serve this any more. It's awful."
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