5 ms·

> If my definition of infinity is the set of all integers, ... The cardinality of the set of integers is aleph-0. Aleph-0 is one of many transfinite cardinals

• deleted 13y ago
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• gizmo686 13y ago
  To anyone studing calculus: lim{x -> ∞} (2x)/(3x) != (2 * infinity) / (3 * infinity) In fact, the infinities we are speaking of are two completely different objects. The limit as x-> ∞ is explicitly defined seperatly from the limit as x->(Real Number). In fact this definition makes no further reference to ∞, and instead says that for any arbitrarily small, positive d, there is a real number m such that x>m implies (2x)/(3x) is within m of 2/3. The infinity we are talking about when we say (2 * infinity) / (3 * infinity) = 2/3, (I assume) is the size of the set of integers, which bears no relation to the symbol ∞ used in limits. Ultimately, the important thing to remember in situations like this is that if something has not been defined as true, or proven to be true, you cannot assume it. Many similarities (such as overloading operators) are chosen for convenience, not because they are the same. The problem is that most of the time these similarities were made because there really is a strong parrallel, and you look like an idiot for wasting a math class to prove that 0x=0. (In my case, those two 0s weren't even the same object: the left one was a real number, the right one was a vector)