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I would say $\infty - \infty=0$,because even though $\infty$ is an undetermined number,$\infty = \infty$.so $\infty-\infty=0$.

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    Very relevant: http://en.wikipedia.org/wiki/Indeterminate_form. Hopefully, someone will write a nice answer.2011-08-30
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    @Sri I see no "indeterminate forms" in the question.2011-08-30
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    @Bill I have been implicitly taking that term to include "expressions" of the form $\infty - \infty$, not just algebraic expressions that are obtained in the context of limits (quoting wikipedia here). I guess that's my mistaken belief.2011-08-30
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    @Sri "Infinity" has *many* different meanings in mathematics. As such, the question is ill-posed as it stands.2011-08-30
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    With natural numbers the result of taking $m$ items away from a set of $n$ items, $m\le n$, will result in a set with a *unique* number of items in it (no matter *which* subset of $m$ items were taken away), hence it makes sense to label the result as a specific number, namely $n-m$. With an infinite ($\aleph_0$) set of items, taking away an infinite subset doesn't uniquely determine the cardinality of the resulting set, hence $\infty-\infty$ is ill-defined in this context.2011-08-30
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    Relevant reading: http://math.stackexchange.com/questions/36289/is-infinity-a-number2011-08-30
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    Pacerier: What do you mean by infinity?2011-08-31
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    @Jonas Meyer: There is obviously something you are not telling us prof. What are we missing in the question.2011-08-31
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    Wolfram Alpha comes up as "indeterminate" -- http://www.wolframalpha.com/input/?i=infinity+-+infinity2012-02-21
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    Somehow the Eilenberg-swindle provides an answer.2013-04-08
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    I might be wrong, but infinity is not a number, so you cannot use certain operators on it - such as subtraction.2013-07-27
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    Any time you talk about $\infty$, you are talking about "limits" in some sense.2013-09-25

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