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I know that $\infty/\infty$ is not generally defined It says infinity to the zeroth power. However, if we have 2 equal infinities divided by each other, would it be 1

Infinity refers to something without any limit, and is a concept relevant in a number of fields, predominantly mathematics and physics Your title says something else than infinity times zero The english word infinity derives from latin infinitas, which can be translated as unboundedness , itself derived from the greek word apeiros, meaning endless .

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. Likewise, 1 / 0 is not really infinity Infinity isn't actually a number, it's more of a concept If you think about how division is often described in schools, say, number of sweets shared between number of people, you see the confusion.

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. 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.

Absolutely, infinity has countless (:p) practical applications

Here's one way to think about it Do negative numbers have any practical applications I mean you can't really have a negative amount of anything, can you You can't have negative five apples

If your bank balance is negative, that's just another way of saying you owe the bank a (positive amount of) money, rather than the other. Because multiplying by infinity is the equivalent of dividing by 0 When you allow things like that in proofs you end up with nonsense like 1 = 0 Multiplying 0 by infinity is the equivalent of 0/0 which is undefined.

If any number times zero is zero and any number time infinity is infinity, then what do you get when you multiply zero times infinity

Do they cancel one another out and equal any number since any. 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

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