Skip to comments.Researcher Discovers Longstanding Flaw in Elementary Calculus
Posted on 04/11/2019 1:10:39 PM PDT by johnnyb_61820
This week, WBC fellow Jonathan Bartlett, along with co-author Asatur Zh. Khurshudyan, published a paper showing that elementary calculus contains a longstanding flaw that has been present for over a century. The paper was published in the peer-reviewed journal Dynamics of Continuous, Discrete & Impulsive Systems, Series A: Mathematical Analysis: Mathematical Analysis (DCDIS-A, for short). The journal has been published for a quarter of a century and many major universities across the United States subscribe to it.
The flaw they discovered is one of notation. Now, you may be thinking, how can notation be wrong? Well, notation can be wrong when it implies untrue things, especially when notation exists that implies the correct things.
(Excerpt) Read more at mindmatters.ai ...
Unpossoble! This was settled science.
The technical details: what we thought was ‘=’ is actually ‘!=” (not equals), and what we thought was “!=” is actually “=”.
This has HUGE consequences. It means there *IS* glowBull warming, and that the ‘Rats are correct about *EVERYTHING*. It means Right is Wrong and Left is Right.
Who would have thunk it???
I knew it was insanity trying to solve math equations incorporating the infinity symbol. :)
“I knew it was insanity trying to solve math equations incorporating the infinity symbol. :)”
As did Georg Cantor. :-)
for what I do not an issue!
Crap! Smart ass just made a PANTSLOAD of more work for calc students.
then I want a tax refund!
[...] since dx/dy is the first derivative of x with respect to y, it is easy to see that these values are merely the inverse of each other. The inverse function theorem of calculus states that dx/dy = 1/(dy/dx) . The generalization of this theorem into the multivariable domain essentially provides for fraction-like behavior within the first derivative. Likewise, in preparation for integration, both sides of the equation can be multiplied by dx. Even in multivariate equations, differentials can essentially be multiplied and divided freely, as long as the manipulations are dealing with the first derivative. Even the chain rule goes along with this. Let x depend on parameter u. If one has the derivative dy/du and multiplies it by the derivative du/dx then the result will be dy/dx . This is identical to the chain rule in Lagrangian notation. It is well recognized that problems occur when if one tries to extend this technique to the second derivative [...]
yep the more times I have to put pencil to paper the more mistakes I make!
Yeah because math is always logical.
Crap! Smart ass just made a PANTSLOAD of more work for calc students.Better notation will improve the ability of mathematicians to do advanced work within calculus.
Its well known that Newton invented Calculus, less well known that Liebnitz independently invented Calculus simultaneously, and that who you credited for its invention was a political issue. Brits said Newton, Germans said Liebnitz.I just scanned the paper, and of course, there is no "longstanding flaw" in elementary calculus. . . . I'm not saying it's not interesting, and maybe even useful, but they haven't found a "flaw" in calculus.
Even less well known is that (as a student, IIRC) Charles Babbage rebelled against the teaching of calculus using Newtonian notation. He demanded - and was able to get - calculus to be taught using Liebnitzs notation. Since he was in Britain, you can see that he was cutting against the political grain. But his point was precisely that good notation makes learning/understanding easier. And learning Calculus well via Newtonian notation was harder than it needed to be.
. . . The authors come up with a notation for second (and higher) derivatives that allows elementary calculus formulas to be manipulated in a straightforward way . . . This new notation may even find its way into high school and college calculus courses. - thesharkboy
I tried to explain that to my calculus teacher but he didn't believe me. So he flunked me.........
For ten posts I thought I had an excuse for calculus being difficult for me.
I guess dyslexia will still have to do.
But only if you factor in Janckman’s Plexus and buttonhook the inverse of the third derivative.
Then it all makes sense.
Discovers Longstanding Flaw in Elementary Calculus
I knew it! This explains why I owe money to the IRS every year!
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