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Re: [math_club] Re: help me in these basics

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  • Nasa
    although adding two infinite quantities doesn t make any sense, this is *not* undefined. intuitively, two infinite quantities will result an infinite quantity
    Message 1 of 6 , Feb 1, 2008
      although adding two infinite quantities doesn't make any sense, this is *not* undefined. intuitively, two infinite quantities will result an infinite quantity -- thus the result is clearly infinity. same holds for multiplication.
       
      if you consult the page in wikipedia on defined and undefined quantities (linked from below), you'll see they carefully listed subtraction and division operations to be undefined over two inf quantities, but not addition or multiplication operation. you can check http://en.wikipedia.org/wiki/Indeterminate_form as well, it lists all the indeterminate forms, but again the + and * are missing.
       
      moreover, you can multiply -1 and inf to get -inf and trust me I have seen this several times, why can't you add 2 to inf? consider the prob: lim(x - 2)/(x^2 - 4) as x->inf. try to solve it without interacting a 2 and an inf :) you can find numerous problems in integration where you have to replace for example x+2 with y to solve. how to update the limits if the originals involved inf?
       
      mathmatical rules are defined with a view to making it as general as possible. so we rule out cases only if they can't fit in.
       
      nasa
       

       
      On Jan 31, 2008 11:36 PM, Tanvir Ahamed Bhuyain <tanvirabs@...> wrote:

      INFINITY is not a number. It is just an abstract idea of something
      which cannot be reached or achieved but can only be approached. One
      can not do algebraic operations with infinity because these operations
      are defined only for numbers, variables or other well-defined
      mathematical objects like matrix. So, adding infinity to infinity does
      not mean anything and similarly subtracting, multiplying and anyhting
      else, they are all meaningless.

      Infinity can only be defined as a limit. So, whenever someone talks
      about infinity, it is about a limit. There are no concrete definitions
      for infinty except for the idea of an unreachable limit.

      Also, 2+infinity=infinity does not mean anything. because, you can add
      numbers to "2", which itself is a number, but infinity is not a
      number. so you cannot add infinity to 2.

      Tanvir



      --- In math_club@yahoogroups.com, Nasa <nasarouf@...> wrote:
      >
      > why do we get two simultaneous mails from you?
      >
      > for + and * the result should be inf
      > for the other two, they should be undefined.
      >
      > just as an example:
      > 2+inf=inf => 2=0 if inf-inf=0
      >
      > for more info consult these pages:
      >
      http://en.wikipedia.org/wiki/Defined_and_undefined#Examples_and_workarounds
      > http://en.wikipedia.org/wiki/Infinity
      >
      > you are certainly not talking about limits, but in case anyone is
      > interested, they should consult these pages
      >
      http://en.wikipedia.org/wiki/Limit_of_a_function#Limit_of_a_function_at_infinity
      > http://en.wikipedia.org/wiki/Extended_real_number_line
      >
      > nasa
      >
      > On Jan 30, 2008 10:56 AM, SAAD A <saad_923@...> wrote:
      >
      > > what is the following ans.
      > > infinity+infinity,
      > > infinity-infinity,
      > > infinity*infinity,
      > > infinity/infinity,
      > >
      > > ------------------------------
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    • Tanvir Ahamed Bhuyain
      Infinity is not a number, it s a limiting value which you cannot reach and thus cannot add or multiply. Equations like : infinity+2=infinity or
      Message 2 of 6 , Feb 2, 2008
        Infinity is not a number, it's a limiting value which you cannot reach
        and thus cannot add or multiply.

        Equations like : infinity+2=infinity or infinity*infinity=infinity
        violates the first and most important law of mathematics, that for
        every number "x" there is an unique number "1" and an unique number
        "0" such that x*1=x and x+0=x. Clearly if you allow infinity to be
        used in equations then these laws do not hold, and if these laws do
        not hold then we are back to stone age.

        If you write infinity + 2 = infinity, then what is the definition of
        infinity in this equation? Can you define infinity as a number? If you
        cannot define infinity as a number then you cannot add it to a number.

        for Nasa bhai : In case of limiting functions and integration limits,
        you do not interact infinity with numbers. In calculus these are only
        limits, they cannot be obtained and thus cannot be interacted with.
        for example, the most classic definition of infinity is,
        limit(x=>0)[1/x] = infinity.
        Here, you do not interact 0 with 1 in a division process because that
        is not allowed. You only find the limiting value of 1/x where x is
        approaching 0. So, in your examples you do not interact any number
        with infinity, you only adjust your limits as necessary.

        Of course it is true that adding infinte number of things to infinte
        number things will result in infinite number of things, but that is
        not mathematics, it's philosophy. In mathematics you cannot treat
        infinity as a number of things because you cannot have infinite number
        of things and thus you cannot add infinite number of things

        Tanvir

        --- In math_club@yahoogroups.com, Nasa <nasarouf@...> wrote:
        >
        > although adding two infinite quantities doesn't make any sense, this is
        > *not* undefined. intuitively, two infinite quantities will result an
        > infinite quantity -- thus the result is clearly infinity. same holds for
        > multiplication.
        >
        > if you consult the page in wikipedia on defined and undefined quantities
        > (linked from below), you'll see they carefully listed subtraction and
        > division operations to be undefined over two inf quantities, but not
        > addition or multiplication operation. you can check
        > http://en.wikipedia.org/wiki/Indeterminate_form as well, it lists
        all the
        > indeterminate forms, but again the + and * are missing.
        >
        > moreover, you can multiply -1 and inf to get -inf and trust me I
        have seen
        > this several times, why can't you add 2 to inf? consider the prob:
        lim(x -
        > 2)/(x^2 - 4) as x->inf. try to solve it without interacting a 2 and
        an inf
        > :) you can find numerous problems in integration where you have to
        replace
        > for example x+2 with y to solve. how to update the limits if the
        originals
        > involved inf?
        >
        > mathmatical rules are defined with a view to making it as general as
        > possible. so we rule out cases only if they can't fit in.
        >
        > nasa
        >
        >
        >
        > On Jan 31, 2008 11:36 PM, Tanvir Ahamed Bhuyain <tanvirabs@...> wrote:
        >
        > > INFINITY is not a number. It is just an abstract idea of something
        > > which cannot be reached or achieved but can only be approached. One
        > > can not do algebraic operations with infinity because these operations
        > > are defined only for numbers, variables or other well-defined
        > > mathematical objects like matrix. So, adding infinity to infinity does
        > > not mean anything and similarly subtracting, multiplying and anyhting
        > > else, they are all meaningless.
        > >
        > > Infinity can only be defined as a limit. So, whenever someone talks
        > > about infinity, it is about a limit. There are no concrete definitions
        > > for infinty except for the idea of an unreachable limit.
        > >
        > > Also, 2+infinity=infinity does not mean anything. because, you can add
        > > numbers to "2", which itself is a number, but infinity is not a
        > > number. so you cannot add infinity to 2.
        > >
        > > Tanvir
        > >
        > > --- In math_club@yahoogroups.com <math_club%40yahoogroups.com>, Nasa
        > > <nasarouf@> wrote:
        > > >
        > > > why do we get two simultaneous mails from you?
        > > >
        > > > for + and * the result should be inf
        > > > for the other two, they should be undefined.
        > > >
        > > > just as an example:
        > > > 2+inf=inf => 2=0 if inf-inf=0
        > > >
        > > > for more info consult these pages:
        > > >
        > >
        > >
        http://en.wikipedia.org/wiki/Defined_and_undefined#Examples_and_workarounds
        > > > http://en.wikipedia.org/wiki/Infinity
        > > >
        > > > you are certainly not talking about limits, but in case anyone is
        > > > interested, they should consult these pages
        > > >
        > >
        > >
        http://en.wikipedia.org/wiki/Limit_of_a_function#Limit_of_a_function_at_infinity
        > > > http://en.wikipedia.org/wiki/Extended_real_number_line
        > > >
        > > > nasa
        > > >
        > > > On Jan 30, 2008 10:56 AM, SAAD A <saad_923@> wrote:
        > > >
        > > > > what is the following ans.
        > > > > infinity+infinity,
        > > > > infinity-infinity,
        > > > > infinity*infinity,
        > > > > infinity/infinity,
        > > > >
        > > > > ------------------------------
        > > > > Looking for last minute shopping deals? Find them fast with Yahoo!
        > > Search.<
        > >
        http://us.rd.yahoo.com/evt=51734/*http://tools.search.yahoo.com/newsearch/category.php?category=shopping
        > > >
        > > > >
        > > > >
        > > >
        > >
        > >
        > >
        >
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