
Infinite is easier than big - fogus
http://www.johndcook.com/blog/2010/09/09/infinite-is-easier-than-big/
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Eliezer
As an infinite set atheist, I think it's important to distinguish people who
say "infinite" when they want to talk about the limit of unbounded finite
behaviors ("a Turing machine has an infinitely long tape") and people who say
"infinite" when they want to talk about big collections ("the cardinality of
the collection of real points between 0 and 1"). A smarter language would have
different words for these.

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jgershen
What he's saying is that by "infinite," people usually mean "arbitrarily
large". I've found that if you just say "arbitrarily large" when that's what
you mean, it eliminates a lot of these misunderstandings.

Of course, I talk to a lot of engineers and mathematicians. You run the risk
of sounding unnecessarily pedantic.

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samdk
No he's not, he's saying that infinity is a useful abstraction for dealing
with "arbitrarily large". That often the tools we have for dealing with
infinity can give us a better idea of how things behave in arbitrary large
cases than the tools we have for dealing with smaller, more manageable cases.

His point is that infinity and the tools we have for dealing with it are
useful, not pointless abstractions.

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jgershen
I understand that point and I agree. What I'm saying is that upon reading the
article closely, I noticed he was primarily promoting the "view infinite as
arbitrarily large" technique for dealing with the appearance of infinity.

Example quote from article: "Interpret the problem as saying that the width of
the capacitor is so large relative to its thickness that you don’t have to
worry about edge effects."

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pigbucket
There was a great post and a slightly crazy discussion about infinity and the
Hilbert Hotel here a few months ago:
<http://news.ycombinator.com/item?id=1333424>

The penultimate paragraph of the present post sounds like a conversation you
might hear in one of the infinitely long infinitely many bars at the Hilbert
Hotel:

Nervous Dude: When I went to grad school, my intention was to study functional
analysis. Essentially this means infinite dimensional vector spaces.

Unimpressed Girl: That sounds terribly abstract and useless.

Nervous Dude: But it can be quite practical. My background in functional
analysis served me well when I went on to study partial differential equations
and numerical analysis.

Seriously Unimpressed Girl: Gotcha.

