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- calculus - What is infinity divided by infinity? - Mathematics Stack . . .
One advantage of approach (2) is that it allows one to discuss indeterminate forms in concrete fashion and distinguish several cases depending on the nature of numerator and denominator: infinitesimal, infinite, or appreciable finite, before discussing the technical notion of limit which tends to be confusing to beginners
- calculus - Infinite Geometric Series Formula Derivation - Mathematics . . .
Infinite Geometric Series Formula Derivation Ask Question Asked 12 years, 1 month ago Modified 4 years
- What is the difference between infinite and transfinite?
The reason being, especially in the non-standard analysis case, that "infinite number" is sort of awkward and can make people think about $\infty$ or infinite cardinals somehow, which may be giving the wrong impression But "transfinite number" sends, to me, a somewhat clearer message that there is a particular context in which the term takes
- elementary set theory - What do finite, infinite, countable, not . . .
Clearly every finite set is countable, but also some infinite sets are countable Note that some places define countable as infinite and the above definition In such cases we say that finite sets are "at most countable"
- Does infinite equal infinite? - Mathematics Stack Exchange
(the principal exception I know of is the extended hyperreal line, which has many infinite numbers obeying the 'usual' laws of arithmetic, and a pair of additional numbers we call $+\infty$ and $-\infty$ that have the largest magnitude of all infinite numbers, and do not obey the 'usual' laws of arithmetic)
- Proof of infinite monkey theorem. - Mathematics Stack Exchange
The infinite monkey theorem states that if you have an infinite number of monkeys each hitting keys at random on typewriter keyboards then, with probability 1, one of them will type the complete works of William Shakespeare
- In an infinite sum, is there an actual term at an infinite position?
As for what infinite summation means Zeno's first paradox maps to this very problem Infinite summation shows how an infinite number of terms can sometimes add up to a finite number Edit 2: Per a long conversation in the comments, we found that a misunderstanding about the set of natural numbers is at the heart of the confusion
- When does it make sense to say that something is almost infinite?
A metal beam is not a continuous object, but a finite collection of molecules An economy is not a distribution of wages and trade preferences, but a finite list of governments, firms, and consumers But when these lists are, one might say, almost infinite, we can understand them more readily as their continuous, infinite counterparts
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