6khyati what i said also exists...
but where i dont know:P:P rather no one knows...
Which of these is true?
Infinity a perfect square?
Infinity is a Real Number
Infinity is a Even number
It is an odd number
It is both even and odd
It is neither even nor odd
It is a Integer
It is a rational number
It is an irrational number
The last one [3] It is a mystery [3]
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39 Answers
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341Algebraically 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, an>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
11@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!).
6well infinity is just used as a ref. that it is the greatest among all the nos..
11Well 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.
11anyways 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
6Infinity is a floorless room without walls or ceiling.
thats how i define it!!!
this has been my status on Facebook since days....:P:P
11Kalyan what you said doesnt exist, but infinity exist but no one knows where
1∞ 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.
1actually 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:)
6yeah 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!!!
1guys 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
1Infinity 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
1JUst 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.
341I 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?
62i was trying to be a bit poetic in asking the question you just did [1] [6]
62if it is only a symbol... how can we talk about the limit of something tending to a symbol? what do we in that case mean by infinity if it is just a symbol!
11for 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
11It is a symbol for the behaviour of a variable which continuously changes and passes all limits.
49LOL!! poetic!
hmm....so thus must be the answer!! :P
Infinity is the number beyond the realms of even or odd!
Infinity is the number beyond the realms of rational or irrational!
Fraction of Integer...
and also [3] it is neither real nor mystery [3]
it is the zenith of numerals which everyone tries to comprehend but everyone fails to...
Infinity is the number JUST BEYOND what u have reached while counting → so u can never reach it...
LOL...am i defining INFINITY or GOD??
Infinity can be even or odd or both or none..
same for rationality and it being integer...
but the thing is "it is just beyond human perception and so cannot be classified"
in short infinity is infinity..and it is infinity only...it is not even/odd; rational/irrational; fraction/integer; [3] real/imaginary...reality/mystery...:D
1Infinity is not any number... but just a concept........that we can imagine which is greater than the greatest and smaller than the smallest....