Soundness of Calculus?
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In this wikipedia article. It talks about the "soundness of calculus", but it seems to talk about soundness in an informal sense and how analysis/calculus was not very rigorous and not the soundness in logic it linked to.
My questions is, assuming the article didn't make a mistake, how was Weierstrass's contribution in "modernizing analysis" related to the "soundness of calculus"?
analysis logic soft-question math-history
edited Dec 4 '18 at 17:16
GNUSupporter 8964民主女神 地下教會
12.8k72445
asked Dec 4 '18 at 16:47
SpooFwenSpooFwen
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add a comment |
$begingroup$
In this wikipedia article. It talks about the "soundness of calculus", but it seems to talk about soundness in an informal sense and how analysis/calculus was not very rigorous and not the soundness in logic it linked to.
My questions is, assuming the article didn't make a mistake, how was Weierstrass's contribution in "modernizing analysis" related to the "soundness of calculus"?
analysis logic soft-question math-history
edited Dec 4 '18 at 17:16
GNUSupporter 8964民主女神 地下教會
12.8k72445
asked Dec 4 '18 at 16:47
SpooFwenSpooFwen
597
$endgroup$
$begingroup$
Yrs, it is quite informal; but "soundness" means consistent+true axioms.
$endgroup$
– Mauro ALLEGRANZA
Dec 4 '18 at 17:38
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The issue is with the use of infinitesimals in the calculus with the well-known critique about using "vanishing quantities" in operations, that amounts to dividing by zero. Obviously, dividing by zero is an "unsound" operation.
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– Mauro ALLEGRANZA
Dec 4 '18 at 18:34
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@Mauro ALLEGRANZA if that's what they meant by soundness I guess this more or less answers my question
$endgroup$
– SpooFwen
Dec 4 '18 at 19:17
add a comment |
$begingroup$
In this wikipedia article. It talks about the "soundness of calculus", but it seems to talk about soundness in an informal sense and how analysis/calculus was not very rigorous and not the soundness in logic it linked to.
My questions is, assuming the article didn't make a mistake, how was Weierstrass's contribution in "modernizing analysis" related to the "soundness of calculus"?
analysis logic soft-question math-history
edited Dec 4 '18 at 17:16
GNUSupporter 8964民主女神 地下教會
12.8k72445
asked Dec 4 '18 at 16:47
SpooFwenSpooFwen
597
$endgroup$
In this wikipedia article. It talks about the "soundness of calculus", but it seems to talk about soundness in an informal sense and how analysis/calculus was not very rigorous and not the soundness in logic it linked to.
My questions is, assuming the article didn't make a mistake, how was Weierstrass's contribution in "modernizing analysis" related to the "soundness of calculus"?
analysis logic soft-question math-history
analysis logic soft-question math-history
edited Dec 4 '18 at 17:16
GNUSupporter 8964民主女神 地下教會
12.8k72445
asked Dec 4 '18 at 16:47
SpooFwenSpooFwen
597
edited Dec 4 '18 at 17:16
GNUSupporter 8964民主女神 地下教會
12.8k72445
asked Dec 4 '18 at 16:47
SpooFwenSpooFwen
597
edited Dec 4 '18 at 17:16
GNUSupporter 8964民主女神 地下教會
12.8k72445
edited Dec 4 '18 at 17:16
GNUSupporter 8964民主女神 地下教會
12.8k72445
edited Dec 4 '18 at 17:16
GNUSupporter 8964民主女神 地下教會
12.8k72445
12.8k72445
asked Dec 4 '18 at 16:47
SpooFwenSpooFwen
597
asked Dec 4 '18 at 16:47
SpooFwenSpooFwen
597
asked Dec 4 '18 at 16:47
SpooFwenSpooFwen
597
597
$begingroup$
Yrs, it is quite informal; but "soundness" means consistent+true axioms.
$endgroup$
– Mauro ALLEGRANZA
Dec 4 '18 at 17:38
$begingroup$
The issue is with the use of infinitesimals in the calculus with the well-known critique about using "vanishing quantities" in operations, that amounts to dividing by zero. Obviously, dividing by zero is an "unsound" operation.
$endgroup$
– Mauro ALLEGRANZA
Dec 4 '18 at 18:34
$begingroup$
@Mauro ALLEGRANZA if that's what they meant by soundness I guess this more or less answers my question
$endgroup$
– SpooFwen
Dec 4 '18 at 19:17
add a comment |
$begingroup$
Yrs, it is quite informal; but "soundness" means consistent+true axioms.
$endgroup$
– Mauro ALLEGRANZA
Dec 4 '18 at 17:38
$begingroup$
The issue is with the use of infinitesimals in the calculus with the well-known critique about using "vanishing quantities" in operations, that amounts to dividing by zero. Obviously, dividing by zero is an "unsound" operation.
$endgroup$
– Mauro ALLEGRANZA
Dec 4 '18 at 18:34
$begingroup$
@Mauro ALLEGRANZA if that's what they meant by soundness I guess this more or less answers my question
$endgroup$
– SpooFwen
Dec 4 '18 at 19:17
$begingroup$
Yrs, it is quite informal; but "soundness" means consistent+true axioms.
$endgroup$
– Mauro ALLEGRANZA
Dec 4 '18 at 17:38
$begingroup$
Yrs, it is quite informal; but "soundness" means consistent+true axioms.
$endgroup$
– Mauro ALLEGRANZA
Dec 4 '18 at 17:38
$begingroup$
The issue is with the use of infinitesimals in the calculus with the well-known critique about using "vanishing quantities" in operations, that amounts to dividing by zero. Obviously, dividing by zero is an "unsound" operation.
$endgroup$
– Mauro ALLEGRANZA
Dec 4 '18 at 18:34
$begingroup$
The issue is with the use of infinitesimals in the calculus with the well-known critique about using "vanishing quantities" in operations, that amounts to dividing by zero. Obviously, dividing by zero is an "unsound" operation.
$endgroup$
– Mauro ALLEGRANZA
Dec 4 '18 at 18:34
$begingroup$
@Mauro ALLEGRANZA if that's what they meant by soundness I guess this more or less answers my question
$endgroup$
– SpooFwen
Dec 4 '18 at 19:17
$begingroup$
@Mauro ALLEGRANZA if that's what they meant by soundness I guess this more or less answers my question
$endgroup$
– SpooFwen
Dec 4 '18 at 19:17
add a comment |
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$begingroup$
Yrs, it is quite informal; but "soundness" means consistent+true axioms.
$endgroup$
– Mauro ALLEGRANZA
Dec 4 '18 at 17:38
$begingroup$
The issue is with the use of infinitesimals in the calculus with the well-known critique about using "vanishing quantities" in operations, that amounts to dividing by zero. Obviously, dividing by zero is an "unsound" operation.
$endgroup$
– Mauro ALLEGRANZA
Dec 4 '18 at 18:34
$begingroup$
@Mauro ALLEGRANZA if that's what they meant by soundness I guess this more or less answers my question
$endgroup$
– SpooFwen
Dec 4 '18 at 19:17