infinity?

khyati what i said also exists...
but where i dont know:P:P rather no one knows...

Algebraically speaking the real numbers form a field. http://en.wikipedia.org/wiki/Field_(mathematics).

That means they obey certain rules concerning the operations + and * and have certain properties like unique identity elements under the operations, and unique inverse elements for non-zero elements. The elements ∞ and -∞ do not obey these rules casting them out of the field of real numbers. They form part of the extended real number system which is not a field.
http://en.wikipedia.org/wiki/Extended_real_number_line features the rules obeyed by these elements under the arithmetic operations of real numbers.

So how do we reconcile the use of these symbols in mathematics. Are they merely symbols? To answer this, we have to examine the notion of a number. Modern mathematics uses set theory to define natural numbers using sets and the concept of "successors". For a brief read consult http://en.wikipedia.org/wiki/Natural_number and for a readable but comprehensive exposition the book Naive Set Theory by Halmos.

Then, we have the construction of the rational numbers Q. You are already familiar with the notion that rational numbers have "gaps" between them. What this means becomes clear, when you represent numbers as limits of sequences of rational numbers. Thus a number is actually a symbol for the set of all sequences that converge to a particular number. Thus it becomes possible to fill in these gaps, thus forming the set of real numbers.

Now, we can define ∞ as a symbol for all sequences with the property that given any real number K, we can find a natural number N, such that for all n≥N, a_n>K where a is a sequence which is a member of this set.

-∞ denotes sequences where eventually the sequence can be made lesser than any given real number K.

To settle the debate on whether these numbers are rational or not, you can see the construction of real numbers from rational numbers using the concept of Dedekind Cut.

http://en.wikipedia.org/wiki/Construction_of_the_real_numbers#Construction_by_Dedekind_cuts

You can see that the partition sets A and B are not allowed to be empty. That means ∞ and -∞ are not real numbers and hence rational or irrational do not apply to these symbols

@vishuboy.Well, the reason for infinity to not exist on the no line is that,it is greater than the greatest imaginable no.That's why, while defining an infinite set we always use ) instead of ] (eg:[1,∞)) because no number on the no line can be equal to infinity. Suppose we define 999999999999999999999999999999 as infinity then someone else would define it as 9999999999999999999999999999999(one more 9!).

I think Infinity (∞) ε [All the Given Options]

anyways its good, its make the solution of many question shorter and easier, as in summation

of infinite series in G.P(I gave the example because I know if no one asks but Vivek will definitely ask saying as in.........):P ;) :P

actually frndz infinity dependz on the max limit that u can thnk and the max no.wat u can imagine dependz on ur imagination power whether its an even or ood!!!!!!!!!!!or god:)

yeah right

infinity is a relative term...

for a no like 1 a no like 999999999999999999 is infinity

but for a decimal quantity like 0.000000000000000001 1 is infinity!!!

infinity is a point where two parallel lines meet

but point cant be even or odd u see frn.......or a decimal even??

Infinity is God. It exists, it can be felt, many solutions tend to infinity just as many men and women approach the God, but it cannot be defined the way God cannot be defined

JUst like PCs, cars, rockets, all modern machines run of software, physics chemistry etc all run of mathematics. It is universal software to run all subjects.

for infinity to be even
lim (x/2)
x→∞
must be some number but limit is undefined so it is not a even number similarly it is not a ood

see

srinivasan ramanujan's lectures on GOD , ZERO AND INFINITY...