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Old 2015-07-12, 11:03   #1
wildrabbitt
 
Jul 2014

22·3·37 Posts
Default 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.



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Old 2015-07-12, 11:20   #2
xilman
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Quote:
Originally Posted by wildrabbitt View Post
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
It means "as the limit tends to 1 from below". The plus sign version would mean "from above".
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Old 2015-07-13, 06:37   #3
wildrabbitt
 
Jul 2014

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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, ....
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Old 2015-07-13, 14:18   #4
wildrabbitt
 
Jul 2014

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It's something to do with the complex numbers involved right?
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Old 2015-07-13, 22:20   #5
TheMawn
 
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May 2013
East. Always East.

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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 2015-07-13 at 22:23
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Old 2015-07-13, 22:32   #6
R.D. Silverman
 
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Nov 2003

22·5·373 Posts
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Quote:
Originally Posted by TheMawn View Post
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.
get me a shovel.
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Old 2015-07-13, 23:03   #7
xilman
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Originally Posted by R.D. Silverman View Post
get me a shovel.
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 2015-07-13 at 23:04 Reason: Fix quoe
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Old 2015-07-14, 00:55   #8
only_human
 
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Quote:
Originally Posted by xilman View Post
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.
A shovel would be more practical in Pamplona.
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Old 2015-07-14, 10:07   #9
wildrabbitt
 
Jul 2014

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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.
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Old 2015-07-14, 11:02   #10
xilman
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Quote:
Originally Posted by wildrabbitt View Post
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, ....
Ok, let's try to give you another hint. The function b(t) is stated to be a continuously differentiable function on the interval [1,x].

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) light-hearted frippery.
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Old 2015-07-14, 11:14   #11
wildrabbitt
 
Jul 2014

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Thanks. It was mostly a reverse psychological ruse to get some more help.
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