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发表于 2015-2-20 16:10
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回复elim:那不是文章而是讨论专题的题目和主要论点:
What is limit theory, does limit theory need basictheory, what is it?
There are two reasonable limit operations in present sciencetheory system:
(1) During the whole process in dealing with infinitesubstances (infinitesimals) in limit calculations, no one dare to say “let thembe zero or get the limit”. So, the infinitesimals in the calculating operationswould never be too small to be out of the calculations and the calculationsdealing with infinitesimals would be carried our forever. This situation hasbeen existing in mathematics since antiquity------ those items of Un--->0never be 0 all the time and Harmonic Series is divergent, so we can produceinfinite numbers bigger than 1/2 or 1 or 100 or 100000 or10000000000 or… from infinite Un--->0 itemsinHarmonic Series and change an infinitelydecreasing Harmonic Series with the property of Un--->0 into any infiniteconstant series with the property of Un--->constant or any infinitelyincreasing series with the property of Un--->infinity. Here we have one of the modernversions of ancient Zeno’s Paradox.
(2) During the process in dealing with infinite substances (infinitesimals)in limit calculations, someone suddenly cries “let them be zero or get thelimit”. So, all in a sudden the infinitesimals in the calculations become toosmall to stay inside the calculations, they should disappear from (be out of)any limit calculation formulas immediately. This situation has been existing inmathematics since antiquity-------those items of Un--->0 must be 0 from sometime and Harmonic Series is not divergent, so we cannotproduce infinite numbers bigger than 1/2 or 1 or 100 or 100000 or 10000000000 or…from infinite Un--->0 items in Harmonic Series. But if it is convergent, anotherparadox appears.
But when and why shouldor should not people treat infinitesimals appearing in infinite numeral cognitions thatway? Does limit theory need basic theory, what is it? |
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