Talk:Cauchy Condensation Test
If all the terms $a_n$ are positive, then why is the sequence of partial sums decreasing... It appears that the pictures need to be redrawn (with the dotted line more like the square root function). --Lord_Farin 12:33, 20 February 2012 (EST)
- Sorry, the dotted line is a graph of $a_n$, not $\sum a_n$. I tried to fix every instance of my mistake, please double check. --GFauxPas 12:39, 20 February 2012 (EST)
- I think the best way to look at the geometric proof is to view the series as a sum of each term in the sequence times one, so you get lots of rectangles of width one that are smaller than the rectangles of the condensed sequence.. If I actually drew that it would be too hard to read the diagram, but now that I think about it it's not that obvious from the current presentation. Suggestions? --GFauxPas 12:59, 20 February 2012 (EST)
- I get it; I think that's cleared now. Minor suggestion would be to use the letter $a$ instead of $f$, as to avoid possible confusion on what it means. --Lord_Farin 13:03, 20 February 2012 (EST)
- I considered that, but I wasn't sure if $a_{2^n}$ was readable enough. Or perhaps you mean $a\left({2^n}\right)$? --GFauxPas 13:04, 20 February 2012 (EST)
- I get it; I think that's cleared now. Minor suggestion would be to use the letter $a$ instead of $f$, as to avoid possible confusion on what it means. --Lord_Farin 13:03, 20 February 2012 (EST)
- I think the best way to look at the geometric proof is to view the series as a sum of each term in the sequence times one, so you get lots of rectangles of width one that are smaller than the rectangles of the condensed sequence.. If I actually drew that it would be too hard to read the diagram, but now that I think about it it's not that obvious from the current presentation. Suggestions? --GFauxPas 12:59, 20 February 2012 (EST)
- The latter. I understood you did it for readability indeed. --Lord_Farin 13:08, 20 February 2012 (EST)
- I edited the proof to explicitly tell the reader about the implied rectangles with width 1. If you can think of a way to make it clearer, please do so. --GFauxPas 13:16, 20 February 2012 (EST)
I don't think it's worth bothering with Rule of Assumption outside of the field of basic propositional logic. What does anyone else think? --prime mover 15:43, 23 February 2012 (EST)
- That seems reasonable, it's being used all the time in proofs implicitly anyway. --GFauxPas 16:00, 23 February 2012 (EST)
Links to group theoretical results
The link to Powers of Group Elements seems out of place here. A student of analysis need not be bothered with the details of abstract algebraical matters for something as mundane as powers of two. I'm fairly sure there is some basic arithmetical result that could be linked to - if not, there need to be one. Failing that, leaving it blank works for me in this particular context. --prime mover (talk) 14:57, 15 February 2013 (UTC)