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

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• 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,
> >
> > ------------------------------
> > Looking for last minute shopping deals? Find them fast with Yahoo!
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> >
> >
>

• 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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