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- Jan 30, 2012

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Also, does anybody know what this integral is called?

- Thread starter Evgeny.Makarov
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- Thread starter
- #1

- Jan 30, 2012

- 2,492

Also, does anybody know what this integral is called?

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- Jan 30, 2012

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To be sure, the question is a little
, but there is a perfectly reasonable answer.

@Evgeny.Makarov

I will certainly yield to you on any question of logic.

But here is my research area.

Those of us in the H.S.Wall/Gilliam tradition have no idea what $\int f $ means,

We know what $\int_a^b f $ means.

Sorry to say, I find your question meaningless.

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Edit: And why is it that you know what $\int_a^bf$ means but don't know what $\int f$ means?

Sorry, but as an member of what is generally call the "Texas school" I find that a meaningless expressionism.For $\displaystyle\int\frac{dx}{dx}$ to make sense, the expression after the integral sign must have a single $dx$ in the nominator. Therefore, $dx$ in the denominator is not a differential, but rather a product of a constant $d$ and a variable $x$. Therefore, $\displaystyle\int\frac{dx}{dx}=\frac{\ln|x|}{d}+C$.

I understand that logicians take liabilities in defining notations.

But I am not ready to give you free rain with this this one.

Some of us have had to give in to publishers in order of get textbooks out.x And why is it that you know what $\int_a^bf$ means but don't know what $\int f$ means?

That simply means

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This question was told to me by fellow students probably during my first or second year, even before I chose to specialize in logic.I understand that logicians take liabilities in defining notations.

I think also that lateral thinking used here can be useful not so much in mathematics, but in programming, where programs sometimes parse not according to common sense. I don't have a good example right now; if I come up with one, I'll post it here.

Then I think $\int f$ should denote the antiderivative and $\int^b_a f$ should not make sense.That simply meansanti-derivative.

Anti-derivativeis not integral,

It's tricky the solution. And I did not expected to have such a simple answer.

For an example of how programs parse do you refer to something like this (in C):

(0 && (b=getch()), where if some compiling time optimizations are set, the program will not read b?

/* let's say we know a*a+b*b>0 */

/* let's say we are satisfied with a very rough approximation*/

#define infinity 4294967295

if (( a = getValue() ) && (( b = aVeryResourceIntensiveComputation() ))

{ c = b/a; }

else

{ c = infinity;}

makeSomeVeryRoughApproximation(c);

For an example of how programs parse do you refer to something like this (in C):

(0 && (b=getch()), where if some compiling time optimizations are set, the program will not read b?

/* let's say we know a*a+b*b>0 */

/* let's say we are satisfied with a very rough approximation*/

#define infinity 4294967295

if (( a = getValue() ) && (( b = aVeryResourceIntensiveComputation() ))

{ c = b/a; }

else

{ c = infinity;}

makeSomeVeryRoughApproximation(c);

Last edited:

If you can find the first edition ofThen I think $\int f$ should denote the antiderivative and $\int^b_a f$ should not make sense.

$\int^b_a f$ is used for an integral.

Gillman is known as a stickler for correctness of notation. After all he was brought to Texas to fill the void created by the forced retirement of R.L. Moore.

If you can find an actual copy of that text, you will see my pick for the best ever calculus textbook. The size of the book is totally reasonable; the typography is beautiful; there is no need for technology.

Most importantly, Gillman develops the integral by way of a betweeness property.

As a side bar: I think that Gillman is the only MAA president who was also a Julliard graduate.