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]

well infinity is just used as a ref. that it is the greatest among all the nos..

As for example? :P

Well infinity is something that can put us in infinite confusion (of course, if someone thinks a

lot about it) for a longer period of time.

∞ didn't have a place earlier but now the number line has been modified to incorporate the two ∞ s. It's called Extended number line.

Ironically... our books state it to be a number line where it had to be Extended number line :P. Coz, the usual number line is only limited to real numbers but in our calculations, we often use the -∞ and +∞ notations on the number line.

As said earlier, it's more of an idea and not a mere number, it doesn't come under any set of numbers and often is helpful in finding limiting values in calculus.

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!!!

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

guys just chill
infinity is just a relative term. for example see in physics we say that for an object at infinity the the image by a concave mirror is formed at infinity right but as we did the experiments in class 10 to find the focal length of a mirror the object was hardly a few meter away butt compared to the focal length of the mirror it was infinite. For an ant a distance of about 100 meters seems to be infinity but thats not the case with us. So u just cant reach a point on the number line and say "yipee i reached infinity " coz the infinity is still at inifinite distance from u. Its's derivative cannot be defined coz it's value can never be represented as an function. Hope this clears all the mess

I wonder about that last statement(in post #1): why is there a doubt as to whether ∞ is irrational or not?

Again, which number is not a symbol?

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

It is a symbol for the behaviour of a variable which continuously changes and passes all limits.