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#193883 - 11/08/10 03:10 PM Suffix "-esimal"  
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TheFallibleFiend Offline
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TheFallibleFiend  Offline
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(Mostly from http://www.etymonline.com/)

Finite comes from Latin for "boundary."

"In-" as in "infinite" means "without," so "infinite" is "without boundary."

"-tude" as in "infinitude" is "state" or "state of" so "infinitude" is "state of infinity"

"-y" as in "infinity" means "quality or condition or state"
(etymology 3 at http://en.wiktionary.org/wiki/-y)

So "infinity" is "state of being infinite."
Same for "-ness."

Apparently, neither "-y" nor '-ness' is Latin. (Not that I care - just observing.)

However, I'm not sure where "-esimal" comes in. "Infinitesimal" was coined (according to the refs and what I've heard) by Leibniz. Seems to mean something like "part of." So infinitesimal could mean "infinith part of" which seems to fit.

Any ideas?

#193884 - 11/08/10 03:53 PM Re: Suffix "-esimal" [Re: TheFallibleFiend]  
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zmjezhd Offline
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zmjezhd  Offline
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Latin -esimus means the same as English -th, i.e., ordinal rank: e.g., centesimus '100th', millesimus '1000th'. Infnitesimal means something like 'the infinith (rank)'. There are examples in Classical Latin of -esimus being used with non-numbers: e.g., multesimus 'trifling',


Ceci n'est pas un seing.
#193895 - 11/08/10 08:40 PM Re: Suffix "-esimal" [Re: TheFallibleFiend]  
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TheFallibleFiend Offline
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Makes sense. Archimedes developed a method of computing areas under a curve by dividing the area into a bunch of rectangles. Of course this is only an approximation, depending on how you draw the rectangles, the actual area is slightly more or less than the sum of the rectangles. http://www.squarecirclez.com/blog/riemann-sums/4715

OTOH, if you take the width of each rectangle to be an very small, and then perform the sum, the error is arbitrarily small, approaching zero in the (infinitesimal) limit.

#193937 - 11/10/10 02:30 PM Re: Suffix "-esimal" [Re: TheFallibleFiend]  
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So anyway the definition of integrate at

http://www.etymonline.com/index.php?term=integrate

is "to put together parts or elements and combine them into a whole." In the mathematical sense, it's clear that integration is a putting together of the elements (long thin rectangles) to determine the whole (sum) of the area under a curve.

In the social sense, racial integration is also making a whole of the separated parts of society.


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