IIT JEE , AIEEE Forum - Mathematics , Algebra

neeraj_agarwal_1990

anything divided by 0 is NOT DEFINED

any expression involving infinity is also NOT DEFINED

eg. 0/0 , 1/0 ,infinity , infinity x zero , 0/infinity etc...

but
(no. tending to 0 / no. tending to 0) is an indeterminate form....
similarly...
(no. tending to infinity / no. tending to infinity) is indeterminate

0 /no. tending to inf is exactly equal to 0

(no. tending to 0 / no. tending to infinity) is a no. approaching 0...

and so on...

umang

here's a query regarding infinite series
consider f(x) = 1- x + x^2 - x^3 + x^4 -....till infinity
now f(1)=1-1+1-1+1-1.....
this should come either 1 or -1
but if u use infinite GP formula answer comes out to be 1/2
pls explain !!!!!

papu071291

infinity cannot be defined but it is biggest of all numbers.
0/0 canoot be defined exactly it is undefined.

1/0 is an infinity

maani

in my views
INFINITY is
one more that the limit of KNOWN numbers

eg.if u think 100000000000000000 as ur last number of ur counting limit
and then add 1 will be infinity
and if you add 1 more
then on adding 1 more will be ur infinity
and so on............

so INFINITY is 1 more than your known counting limit

btetarbe

Hey md_2674062, something/infinity is never equal to zero but is only approximated to be zero,
Suppose   1/10 = 0.1
                1/100 = 0.01
                1/1000 = 0.001
Like this you go on forever,
     You will start to get 10^-99, 10^-100 , 10^-101 and so on. Thus when we take this to infinity, we start to assume it as 0.

neeraj_agarwal_1990

1/0 is not INFINITY!!!!!

VivekMSC

I am a little bit surprised to see the confusion between infinity, undefined here taking 0/0 etc.

Infinity is an undefined quantity and thus lies outside the set of Real Numbers and thus can't be defined quantitatively despite the fact that it has a qualitative meaning.

The 7 forms 0/0, etc. are "indeterminate" forms. They can't be determined and so the question of definition does not arise.

A "divide by zero" is essentially undefined and not strictly infinity because infinity itself is undefined. You can't give an answer and say "this is it" when the answer itself is not defined. That is why limits which evaluate to "infinity" are essentially answered as "limit does not exist" and not "limit is infinity" because limit gives us a quantitative idea of the function and infinity is not quantitatively defined.

VivekMSC

@Umang

Infinite GP formula is for a converging series. The common ratio for a converging series is |r|<1 and so your example does not satisfy that requirement.

younggenius

infinity is a symbol which denotes a number that cant e found out.
Also 0/0is indeterminate which means it can take any value in R

umang

ok
so whats the f(1) ?

Raghudevan

infinty is not a real number that can be compared with real numbers just as complex numbers. but we regard it as the greatest value, that is greater than any value that we can imagine. its basically undefined for the need of some vlaue greater than any we can think of.

0/0 is not defined as it does not make sense to divide nothing by nothing.

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