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Infinity minus infinity

The calculation of infinity minus infinity has as result not zero, but is

 


Explanation

Infinity is not a number, and has no fixed value. The calculation

∞ − 1 = ∞

shows this. You could write

∞ − ∞ = 1          

but that is incorrect. Because you can also calculate

∞ − 2 = ∞

and then you would get

∞ − ∞ = 2          

It can have any value (also zero) and is therefore undefined.

 


Example 1

The equation

has three solutions

You can see the intersection points in the chart.

Let's do something special, and take

because that is undefined. In the chart you can see that there are indeed only three intersection points.

 


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