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Infinity minus Infinity 
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#1
Mar2507, 03:48 PM

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Does subtracting infinity from infinity leave you with zero?
Or could you subtract infinity from infinity and still have infinity? 


#2
Mar2507, 03:52 PM

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Subtracting infinity from infinity has no mathematical meaning. Unless we are talking about limits and orders of magnitude.



#3
Mar2507, 04:00 PM

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Let N be the natural numbers and R be the real numbers. And card(X) denote the cardinality of X. card(R) + card(N) = card(R) card(N) + card(N) = card(N) 


#4
Mar2507, 04:14 PM

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Infinity minus Infinity
Some examples: The extended real line contains two points "at infinity": [itex]+\infty[/itex] and [itex]\infty[/itex]. The extended real line also comes with a notion of subtraction that's defined for most, but not all arguments. [itex](+\infty)  (\infty) = +\infty[/itex] and [itex](\infty)  (+\infty) = \infty[/itex], but [itex](+\infty)  (+\infty)[/itex] and [itex](\infty)  (\infty)[/itex] are undefined. (And any combination involving at least one finite number is defined) In the cardinal numbers, there are lots of infinite cardinals. (literally, too many to count) Subtraction makes little sense for them, because if [itex]\alpha \leq \beta[/itex] and [itex]\beta[/itex] is infinite, then [itex]\alpha + \beta = \beta[/itex]. The hyperreal line contains many infinite and infinitessimal numbers, and in a certain sense, the hyperreals behave exactly like the reals. (e.g. you can subtract any hyperreal from any other hyperreal) 


#5
Mar2507, 06:36 PM

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