Turn on thread page Beta

The sum of all the positive integers = watch

Announcements
    • Thread Starter
    Offline

    3
    ReputationRep:
    -1/12

    Discuss.
    Offline

    0
    ReputationRep:
    :confused: meh?
    Offline

    0
    ReputationRep:
    no, you're wrong, it';s not negative!
    Offline

    12
    ReputationRep:
    (Original post by AntiMagicMan)
    -1/12

    Discuss.
    The Sum of all +ve integers = +ve Infinity
    • Thread Starter
    Offline

    3
    ReputationRep:
    . Try again. Do some research into the Riemann Zeta function and how s(-1) is evaluated.
    Offline

    0
    ReputationRep:
    s(-1) is outside the domain for which Euler's interpretation is valid. They've used "analytic continuation" to get -1/12 which doesn't really sound too hot...
    • Thread Starter
    Offline

    3
    ReputationRep:
    Yep, thats right.

    But in physical problems when the answer needs to take it into account this interpretation of the sum of all positive integers actually works and agrees with experimentation!
    Offline

    0
    ReputationRep:
    Seems pretty counter-intuitive that it's:
    a) negative,
    b) a fraction.

    Doesn't the Reimann thing just deal with complex numbers anyways?
    • Thread Starter
    Offline

    3
    ReputationRep:
    -1 is a complex number.
    Offline

    0
    ReputationRep:
    lol i think theres a thread for that http://www.uk-learning.net/t56272-2.html
    • Thread Starter
    Offline

    3
    ReputationRep:
    Yes .
    Offline

    0
    ReputationRep:
    by the way, which physics problems need the sum of all positive numbers to equal -1/12?
    Offline

    0
    ReputationRep:
    Here's physicists for you :rolleyes:
    Offline

    3
    ReputationRep:
    (Original post by beauford)
    Here's physicists for you :rolleyes:

    ? :confused:
    Offline

    0
    ReputationRep:
    Soz to resurrect a dead thread but which physics experiments need the sum to be -1/12 Magic?
    Is it used in the Casmir effect?
    Are there others?
    Offline

    11
    ReputationRep:
    (Original post by llduncanll)
    Soz to resurrect a dead thread but which physics experiments need the sum to be -1/12 Magic?
    Is it used in the Casmir effect?
    Are there others?
    Yes, Casimir effect needs it. Check out the Wikipedia for more (the paragraph called "Applications").
    Offline

    14
    ReputationRep:
    that the one where two plates of metal are attracted by quantum vacuum fluctuations? :confused: the weird just got weirder...
    Offline

    12
    ReputationRep:
    I don't see how the addition of an infinite number of +ve integers leads to a negative fraction when:

    There are no -ve values in the addition
    There are no fractional values in the addition

    Load of rubbish.
    Offline

    11
    ReputationRep:
    (Original post by mik1a)
    that the one where two plates of metal are attracted by quantum vacuum fluctuations? :confused: the weird just got weirder...
    Yup, that's the one. I must admit I dismiss quantum mechanics quite readily, because it's just too unreal for me.
    Offline

    0
    ReputationRep:
    (Original post by Invisible)
    I don't see how the addition of an infinite number of +ve integers leads to a negative fraction when:

    There are no -ve values in the addition
    There are no fractional values in the addition

    Load of rubbish.
    Yeh, common sense does seem to suggest it's wrong.
 
 
 
Turn on thread page Beta
Updated: August 11, 2004

University open days

  1. Norwich University of the Arts
    Undergraduate Open Days Undergraduate
    Fri, 28 Sep '18
  2. Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 29 Sep '18
  3. Birmingham City University
    General Open Day Undergraduate
    Sat, 29 Sep '18
Poll
Which accompaniment is best?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.