However, if we have 2 equal infinities divided by each other, would it be 1 So the question would be, when n tends to +infinity does t also tend to +infinity The infinity can somehow branch in a peculiar way, but i will not go any deeper here
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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
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? 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. 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 Limit when zero divided by infinity ask question asked 10 years, 1 month ago modified 8 years, 5 months ago Infinity divided by infinity ask question asked 7 years, 9 months ago modified 7 years, 9 months ago Any number raised to the power of infinity [closed] ask question asked 14 years ago modified 7 years, 1 month ago
In particular, infinity is the same thing as 1 over 0, so zero times infinity is the same thing as zero over zero, which is an indeterminate form
Your title says something else than infinity times zero It says infinity to the zeroth power. 1 / (e raised to t), while t tends to +infinity = 0 However, 0 times infinity is indeterminate form right
