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Izzhov
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[tex] x^2=x+x+ ... +x [/tex] (with x terms). Its derivative is [tex] 1+1+ ... +1 [/tex] (also x terms). By this logic, [tex] \frac{d}{dx} x^2=x [/tex] But it doesn't. So what's wrong with this picture?
Izzhov said:[tex] x^2=x+x+ ... +x [/tex] (with x terms).
Izzhov said:You didn't really help much!
You didn't think much. Matt Grime's purpose was to give you something to think about- that's always a great help.Izzhov said:You didn't really help much!
That is not the calculation you used before: you said "x2= (x+ x+ ...+ x) (x times)". That is not the same as saying "add [itex]\pi[/itex] to itself 3 times, then add [tex] (\pi - 3) \ast \pi [/tex]." That was d_leet's point. Why do you mean by "[itex]\pi[/itex] added to itself [itex]\pi[/itex] times"?Izzhov said:Listen: I have thought about it, contrary to what people may think! If x is [tex] \pi [/tex], for example, you just add [tex] \pi [/tex] three times and then add [tex] (\pi - 3) \ast \pi [/tex] and you get [tex] \pi^2 [/tex]. I don't see the problem with applying this method to any real number.
Izzhov said:[tex] x^2=x+x+ ... +x [/tex] (with x terms). Its derivative is [tex] 1+1+ ... +1 [/tex] (also x terms). By this logic, [tex] \frac{d}{dx} x^2=x [/tex] But it doesn't. So what's wrong with this picture?
that kind of vaguely definedMr.4 said:I think the problem itself lies in that there are x terms. I myself find it quite ambiguous but I'm going with it . I'll try and explain:
Since there aare f(x) 'x' terms where f(x) is a function of x. In that we would have to differentiate f(x)*x using fromduct rule which would result: xf'(x)+f(x).
Thus we cannot directly apply derivatives of
Actually pretty well stated.sums becuase the number of such sums is in turn a function of x.
(Well, now! I don't understand that myself! )
HallsofIvy said:My point was not so much that you can't say that "x2= (x+ x+ ...+ x) (x times)" but rather that the derivative of that is not "(1+ 1+ ...+ 1) (x times)". That "(x times)" is another function of x and you haven't "differentiated" that.
Mr.4 said:I think the problem itself lies in that there are x terms. I myself find it quite ambiguous but I'm going with it . I'll try and explain:
Since there are f(x) 'x' terms where f(x) is a function of x. In that we would have to differentiate f(x)*x using product rule which would result: xf'(x)+f(x).
Thus we cannot directly apply derivatives of sums becuase the number of such sums is in turn a function of x.
(Well, now! I don't understand that myself! )
Izzhov said:Listen: I have thought about it, contrary to what people may think!
If x is [tex] \pi [/tex], for example, you just add [tex] \pi [/tex] three times and then add [tex] (\pi - 3) \ast \pi [/tex] and you get [tex] \pi^2 [/tex]. I don't see the problem with applying this method to any real number.
The flaw in this logic could be that it is based on a biased or incomplete understanding of the topic being researched. It could also be a result of faulty methods or flawed data analysis.
The flaw in a scientific argument can be identified by critically examining the evidence and reasoning presented. This could include checking for any logical fallacies, biases, or inconsistencies in the argument.
Yes, it is possible for a scientific theory to have flaws. Science is an ongoing process of discovery and theories are constantly being revised and improved upon as new evidence and information is gathered.
Some common flaws in scientific studies include small sample sizes, biased or flawed data collection methods, and inadequate control groups. It is important for researchers to be aware of these potential flaws and take steps to minimize their impact on the study.
To avoid falling for flawed logic in scientific arguments, it is important to approach them critically and with an open mind. This means examining the evidence presented, considering alternative explanations, and seeking out multiple sources of information. It is also important to be aware of common logical fallacies and to be skeptical of claims that seem too good to be true.