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Thread: Infinity query

  1. #1 Infinity query 
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    Not being bothered about how big infinity is , can following doubts be cleared ?


    If difference between zero and one is one ,
    Is it possible that , the difference between (infinity/2) and its next number is also ONE.


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  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Infinity is not a real number and cannot be used as one, so the question makes no sense (nor does the successor of infinity).


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  4. #3  
    Brassica oleracea Strange's Avatar
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    The first infinity is the number of integers.

    The next infinity(*) is the number of reals. This is infinitely larger than the first infinity.


    (*) Probably. This has not been proved.
    ei incumbit probatio qui dicit, non qui negat
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  5. #4  
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    series of numbers from 1,2,3,4...................x , difference between each is one. no infinity. X is finite .

    1-2 =-1
    2-1 =1

    (x/2)-((x/2) + 1) = ?


    ((x/2)-1) - (x/2) = ?
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  6. #5  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by sciencestudy View Post
    series of numbers from 1,2,3,4...................x , difference between each is one. no infinity. X is finite .
    Yes, because that is how the natural numbers are defined.

    (x/2)-((x/2) + 1) = ?
    = ((x/2) - (x/2)) - 1 = -1 [Edit: corrected sign]

    ((x/2)-1) - (x/2) = ?
    = (x/2) - 1 - (x/2) = ((x/2) - (x/2)) -1 = -1

    So, what is your point?
    Last edited by Strange; December 11th, 2013 at 05:25 AM. Reason: corrected signs ...
    ei incumbit probatio qui dicit, non qui negat
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  7. #6  
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by sciencestudy View Post
    series of numbers from 1,2,3,4...................x , difference between each is one. no infinity. X is finite .
    Yes, because that is how the natural numbers are defined.

    (x/2)-((x/2) + 1) = ?
    = ((x/2) - (x/2)) + 1 = 1

    ((x/2)-1) - (x/2) = ?
    = (x/2) - 1 - (x/2) = ((x/2) - (x/2)) - 1 = -1

    So, what is your point?
    If ((x/2)-((x/2) + 1) = ?
    = ((x/2) - (x/2)) + 1 = 1= (x/2) - 1 - (x/2) = ((x/2) - (x/2)) - 1 = -1

    So , what is (( x/4)-((x/4)+1)= ?
    (( x/4)-((x/4)-1) = ?
    do you have any idea , what's going on here ?
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  8. #7  
    Genius Duck Dywyddyr's Avatar
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    Quote Originally Posted by sciencestudy View Post
    So , what is (( x/4)-((x/4)+1)= ?
    -1

    (( x/4)-((x/4)-1) = ?
    1

    do you have any idea , what's going on here ?
    Yup.
    You have no idea of mathematics.
    "[Dywyddyr] makes a grumpy bastard like me seem like a happy go lucky scamp" - PhDemon
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  9. #8  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by sciencestudy View Post
    So , what is (( x/4)-((x/4)+1)= ?
    n - (n + 1) = (n - n) - 1 = -1

    For all values of n (x/2, x/4, etc.)

    (( x/4)-((x/4)-1) = ?
    n - (n - 1) = (n - n) + 1 = 1

    For all values of n (x/2, x/4, etc.)

    do you have any idea , what's going on here ?
    I have no idea what you think the problem is. This is basic arithmetic. (Although, embarrassingly, I got the signs wrong in the previous post ... )
    ei incumbit probatio qui dicit, non qui negat
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  10. #9  
    KJW
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    Just to throw a spanner in the works , for a conditionally convergent infinite series such as:



    rearranging the terms can alter the sum.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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  11. #10  
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    Quote Originally Posted by KJW View Post
    Just to throw a spanner in the works , for a conditionally convergent infinite series such as:



    rearranging the terms can alter the sum.
    Thanks for making me relive an embarrassing moment from an undergraduate maths class, where I got this wrong on an exam. The series was presented in a re-arranged form. I re-re-arranged it into the form above, thinking that I was terribly clever to have done so, and wrote down "the" answer by inspection.

    I cringe whenever I recall it. Thanks a lot.
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