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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
- 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
- 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
- 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"
- Uncountable vs Countable Infinity - Mathematics Stack Exchange
As far as I understand, the list of all natural numbers is countably infinite and the list of reals between 0 and 1 is uncountably infinite Cantor's diagonal proof shows how even a theoretically complete list of reals between 0 and 1 would not contain some numbers My friend understood the concept, but disagreed with the conclusion
- Is it valid to use an infinite number of universal existential . . .
My knowledge of logic is very limited, but I am concerned that this approach of "infinite" instantiations is not valid Specifically, it feels like I am trying to use an "inductive step", because for any formal finite proof, I obviously could not explicitly construct this sequence
- infinity - 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)
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