Talk:Euler's Integral Theorem

What is your exact point and your suggestion?

>Why does it follow that $\ds \int_n^N \dfrac {u - \floor u} {u^2} \rd u \le \int_n^N \dfrac 1 {u^2} \rd u$?

Of course, I used $f \le g \implies \int f \le \int g$.

Do you mean I should refer to this result? Or what are you asking, exactly?

At this level of proof, to be realistic, I assume that the reader know some basic like:

$\paren 1$ what is an integral

$\paren 2$ a function that is everywhere continuous except for countable points is integrable

$\paren 3$ an integral is a linear operator, i.e. $\int \paren{f+g} = \int f + \int g$

$\paren 4$ an integral is a positive operator, i.e. $f \le g \implies \int f \le \int g$

Do you mean I should link for everything or only for $\paren 4$? --Usagiop (talk) 14:22, 2 October 2022 (UTC)

Yes. That is what is needed. That is the nature of the site philosophy. --prime mover (talk) 14:35, 2 October 2022 (UTC)

OK, now it should be OK. --Usagiop (talk) 15:26, 2 October 2022 (UTC)