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Are positive infinity and negative infinity equal . There are some proofs which say they are equal and some they are not equal.

Sudhir Saxena

12 Years agoGrade

2 Answers

Saurabh Singh

12 Years ago

This can be answered if we try tosubtractinfinity from infinity .

From a layman's perspective, imagine that I have an infinite number of hotel rooms, each numbered 1, 2, 3, 4, ...

Then I give you all of them. I would have none left, so

8-8=0

On the other hand, if I give you all of the odd-numbered ones, then I still have an infinite number left. So

8-8=8.

Now suppose that I give you all of them except for the first seven. Then

8-8=7.
While this doesn't explainwhythis is indeterminate, hopefully you can agree that itisindeterminate!

hence it would be not right to say that positive infinity and negative infinity are equal. Its like saying a very big positive number is equal to a very big negative number without actually saying what these numbers are. I hope you appreciate and understand the point being made here.

Thanks & Regards

Saurabh Singh,

askIITians Faculty

B.Tech.

IIT Kanpur

shashank

12 Years ago

no its not so....actually they are a bit different... if you consider the no. line then you can easily realise the difference... if you take it to the leftmost side and keep moving then there is your negative infinity and if you keep moving to rightmost side the you will reach to +infinity......u can easily clear your doubt using the concept of limits