20150712, 11:03  #1 
Jul 2014
3×149 Posts 
meaning of 1 with a minus sign at top left, in certain context.
Hi all,
recently I bought a new book. Tenebaum : An introduction to analytic and probabilistic number theory. (from The Cambridge University Press shop in Cambridge!). Those of you who know that I'm midway through a maths degree won't be surprised to hear that I'm stuck on page one. Now, I have a choice : Accept my limitations and get on with what I'm meant to be doing OR don't be so defeatist and drop "The only way one can learn is in a formal, tutor guided & assessed way.", attitude for at least a while. Having eventually changed my mind to the latter, I'm posting here to ask what the little minus means in the two contexts 1) At the top right of the 1 at the bottom of the integral sign of the second integral. and 2) (on the other side of the equation) the same 1 with a minus sign at it's top right involved in the first term which has to be evaluated. http://www.mersenneforum.org/attachm...1&d=1436698800 
20150712, 11:20  #2  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2^{2}·7·397 Posts 
Quote:


20150713, 06:37  #3 
Jul 2014
3·149 Posts 
Thanks.
The thing that I'm confused about is that the interval [1,x] means that x > 1 so I don't understand why the lower limit 1 is tended to from below or the left e.g 9/5 , 8/5, 7/5, .... 
20150713, 14:18  #4 
Jul 2014
3·149 Posts 
It's something to do with the complex numbers involved right?

20150713, 22:20  #5 
May 2013
East. Always East.
11·157 Posts 
In more or less plain english, it means the tiniest possible amount less than 1. For all intents and purposes it is 1, but it could make a slight difference. (EDIT: Well, it DOES make a difference, otherwise they wouldn't bother writing it that way )
For example, 1/0 is undefined, but 1/0^{} tends to negative infinity. Last fiddled with by TheMawn on 20150713 at 22:23 
20150713, 22:32  #6  
Nov 2003
1110100100100_{2} Posts 
Quote:


20150713, 23:03  #7 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2^{2}·7·397 Posts 
Any particular colo{,u}r of shovel?
Sorry. Had far too much (or nowhere near enough) Spanish brandy here tonight on vacation on La Palma. I won't regret this post in the morning^{*} but I may wonder why I bothered to post. Paul * Non, je ne regrette rien as some French bint once said. Last fiddled with by xilman on 20150713 at 23:04 Reason: Fix quoe 
20150714, 00:55  #8  
"Gang aft agley"
Sep 2002
3754_{10} Posts 
Quote:


20150714, 10:07  #9 
Jul 2014
3·149 Posts 
Great. The Mersenne forums where people devote there time and money to finding prime numbers but know next to nothing about maths or aren't willing to share, crack Christmas cracker quality jokes and try to oust eachother from the forums.Really glad
I've spent 10 years testing. 
20150714, 11:02  #10  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2B6C_{16} Posts 
Quote:
Note that b(t) is not stated to be defined only on that interval, only that it is blah blah differentiable on that interval. Now think about such functions. You're just going to have to get used to the (usually) lighthearted frippery. 

20150714, 11:14  #11 
Jul 2014
3·149 Posts 
Thanks. It was mostly a reverse psychological ruse to get some more help.

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