I'm trying to gain a more intuitive understand of the concept of an infinitesimal. When physicists speak of an infinitesimal quantity, if that basically the same as the first order term in a Taylor series expansion of a function they're analyzing?
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1Possible duplicates: http://physics.stackexchange.com/q/70376/2451 , https://physics.stackexchange.com/q/92925/2451 and links therein. – Qmechanic Sep 15 '17 at 15:08
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5Possible duplicate of Rigorous underpinnings of infinitesimals in physics – John Rennie Sep 15 '17 at 15:17
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1You might find this informative as background http://math.blogoverflow.com/2014/11/03/more-than-infinitesimal-what-is-dx/ – Sep 15 '17 at 15:29
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Thank you so much and please accept my apologies for asking a duplicate question. I think I have a much more intuitive appreciation for the concept now. – Steven Sep 15 '17 at 16:08
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I think one good way to get an intuitive feel for an infinitesimal is by means of the following challenge: "You give me any small number, as small as you wish, and I'll give you a number even smaller, and yet, an infinitesimal is smaller even than my number."
If we both start this endless game, we might quickly get bored, but hopefully, we would come away with a sense of where we'd go if we went on forever playing.
A similar challenge could be used to get a sense of the infinitely large, or a sense of what it means to approach an asymptotic limit.
ttonon
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