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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,
by jgershen 16y ago
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.
- samdk 16y agoNo 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.
- jgershen 16y agoI 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."