However, if we have 2 equal infinities divided by each other, would it be 1 If you consider the real numbers as a subset of itself, there is no supremum Can this interpretation (subtract one infinity from another infinite quantity, that is twice large as the previous infinity) help us with things like $\lim_ {n\to\infty} (1+x/n)^n,$ or is it just a parlor trick for a much easier kind of limit?
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Similarly, the reals and the complex numbers each exclude infinity, so arithmetic isn't defined for it
And then, you need to start thinking about arithmetic differently.
Infinity refers to something without any limit, and is a concept relevant in a number of fields, predominantly mathematics and physics The english word infinity derives from latin infinitas, which can be translated as unboundedness , itself derived from the greek word apeiros, meaning endless . The infinity can somehow branch in a peculiar way, but i will not go any deeper here This is just to show that you can consider far more exotic infinities if you want to
Let us then turn to the complex plane Infinity divided by infinity ask question asked 7 years, 9 months ago modified 7 years, 9 months ago Limits and infinity minus infinity ask question asked 5 years, 8 months ago modified 1 year, 6 months ago I understand that there are different types of infinity
One can (even intuitively) understand that the infinity of the reals is different from the infinity of the natural numbers
For infinity, that doesn't work Under any reasonable interpretation, $1+\infty=2+\infty$, but $1\ne2$ So while for some purposes it is useful to treat infinity as if it were a number, it is important to remember that it won't always act the way you've become accustomed to expect a number to act. 7 neither the maximum or supremum of a subset are guaranteed to exist
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