## heuristics vs asymptotics

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• Hello, What is the difference between heuristic data or values and asymptotic data or values. Are these terms interchangeable? If not, how does one
Message 1 of 2 , Apr 14, 2005
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Hello,

What is the difference between heuristic data or values and asymptotic
data or values. Are these terms interchangeable? If not, how does
one distinguish which is proper to use? Curious to any thoughts on
this.

Thanks

-Dick
• ... Heuristics are educated guesses--whenever possible based on solid mathematics, established conjectures and massive computing; but educated *guesses* none
Message 2 of 2 , Apr 14, 2005
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On Thu, 14 Apr 2005, Dick wrote:
> What is the difference between heuristic data or values and asymptotic
> data or values. Are these terms interchangeable? If not, how does
> one distinguish which is proper to use? Curious to any thoughts on
> this.

Heuristics are educated guesses--whenever possible based on solid
mathematics, "established conjectures" and massive computing; but educated
*guesses* none the less.

Asymptote on the other hand are values (functions) that another function
approaches. For example the ration pi(x) / (x/ln(x)) is asymptotic to
1. This is proven. Or more simply, x^2/(x^2+1) is also asymptotic to
1 as x -> infinity.

SO if by asymptotic data you mean data obtained by using asymptotic
approximations (like x/ln(x) for pi(x)) then there is a world of
difference. One can be proven, the other lives in the netherworld of
speculation.

Hope that is of some use...

Chris.
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