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I have seen in some book about extend real number system the following: is |infinity| = |-infinity|= infinity ? When infinity is not a number, how can we think about modulus? Or infinity is number or not. Please discuss. I think infinity is not a number. This is my feeling only. How far I am correct, I really do not know. Please discuss, especially about the modulus of infinity how defined, when infinity is a not a number. Please...

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Hi there! I believe this is an exact duplicate (or along similar lines) of a previous question. As we appreciate questions, we prefer not to have duplicates arise. You may be interested in researching the Extended Real Numbers, the numbers which are used in Calculus implicitly! :-) Furthermore, you may be interested in the mathematical understanding of 'number'; however, that is a very complex topic with a simple beginning. –  000 Dec 5 '12 at 6:39
Sir, I need straight answer for my question. I am not copied this question form any where. Plz try to understand me. –  gama Dec 5 '12 at 6:55
I hope that my answer is 'straight'. If you need any clarification, ask. –  000 Dec 5 '12 at 7:27
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2 Answers

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Usually, when we are working with the extended real numbers, we take continuous functions that are defined on the reals (or some subset) and extended them by continuity to have values at $+\infty$ or $-\infty$ when possible.

In the case of absolute values, we define $|+\infty| = +\infty$ and $|-\infty| = +\infty$ for this reason: i.e. because

$$ \lim_{x \to +\infty} |x| = +\infty \qquad \text{and} \qquad \lim_{x \to -\infty} |x| = +\infty $$

Whether you want to call $+\infty$ and $-\infty$ numbers or not is not really relevant to this situation. I believe that it is very useful to consider them numbers... but maybe that should only be done once you are comfortable doing arithmetic with them.

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!great explanation is given –  gama Dec 5 '12 at 8:37
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Infinity can be a number if you want it to be. Mathematicians can define any sort of number system. What is important is if it's useful and interesting. We see that infinity is not considered a number in the set of real numbers, which is denoted by $\mathbb{R}$. However, in Calculus and other subjects, it helps to informally (sometimes formally) consider infinity a number with a special properties in order to evaluate limits. This number system is called the Extended Real Numbers.

I believe you feel this is simply a yes or no question, and it is not. The answer depends entirely on what you're working with. In some number systems, infinity is defined. In other number systems, infinity is not defined.

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! Thank you so much for your quick explanation. –  gama Dec 5 '12 at 7:28
You are welcome. If you are curious about infinity still (and I hope you are), search 'infinity' in the search bar at the top. All kinds of wonderful questions will come up. :-) –  000 Dec 5 '12 at 7:29
@Limitness! can we put modulus symbol to infinity or not –  gama Dec 5 '12 at 7:36
As far as I know, it is not formally defined and it does not make sense to me. It sounds---to me---like asking what the color of an apple is while looking right at it. I would just say $|\pm \infty|=\infty$, but it doesn't sound particularly set in stone. –  000 Dec 5 '12 at 7:46
Great attempt! +1 for it. :) –  B. S. Dec 7 '12 at 12:09
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