The english word infinity derives from latin infinitas, which can be translated as unboundedness , itself derived from the greek word apeiros, meaning endless . I know that $\infty/\infty$ is not generally defined However, if we have 2 equal infinities divided by each other, would it be 1 Can this interpretation (subtract one infinity from another infinite quantity, that is twice large as the previous infinity) help us with things like limn→∞(1+x/n)n, lim n → ∞ (1 + x / n) n, or is it just a parlor trick for a much easier kind of limit? 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. 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 divided by infinity ask question asked 7 years, 11 months ago modified 7 years, 11 months ago
24 it's pretty straightforward to say that there is an infinite number of different sizes of infinity, but then i thought, what size of infinity is that? my thoughts are that the number of unique cardinalities is equivalent to the number of real numbers, based on the fact that the cardinalities can always be ordered by increasing size. 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.
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