infinity - Comparing Infinities - Mathematics Stack Exchange
2015年8月23日 · Nope, there is no bijection between odd numbers and real numbers. The real numbers are strictly greater in cardinality. Since odd numbers are countable and both are infinite sets, it suffices to show the reals are uncountable, or equivalently that no sequence of reals contains every real (this is done via proof by contradiction).
Limit comparison test for checking the convergence of an infinite ...
2019年11月23日 · The comparison test - Not just for nonnegative series Michele Longo, Vincenzo Valori, October 2003. It seems to me that @user's interpretation of the OP question was different than mine, and she/he seems to have not indicated the relevance (to my interpretation, at least ) of Example 7 in the paper referenced above.
real analysis - Composition of infinite comparison functions ...
2022年9月26日 · Composition of infinite comparison functions. Ask Question Asked 2 years, 3 months ago.
infinity - Are we allowed to compare infinities? - Mathematics …
2016年4月22日 · But there are also an infinite amount of multiples of $2$ and an infinite amount of multiples of $3$, but I don't think there are the same amount of both. The multiples of $2$ are $2,4,6,8,\ldots$ while the multiples of $3$ are $3,6,9,12,\ldots$ So, no matter which number you stop at, the multiples of $2$ will have more numbers.
Comparison of two infinity - Mathematics Stack Exchange
It turns out that not all infinite sets have the same cardinality. The famous early result is due to Cantor. Let $\mathbb{N}$ be the set of positive integers, and let $\mathbb{R}$ be the set of reals. Then $\mathbb{N}$ has cardinality less than $\mathbb{R}$. So, in the sense of cardinality, two infinite sets can have different sizes.
Comparing infinite numbers - Mathematics Stack Exchange
There is no obvious way to bring in some new unit like $\aleph_0$. (2) If you look at constructive approaches to the hyperreals, they essentially involve formalizing the notion of infinite numbers as diverging sequences. There is no obvious way to match up this notion with the set-theoretical notions of cardinals and ordinals.
Limit comparison test for infinite series - Mathematics Stack …
2024年4月5日 · Limit comparison test for infinite series. Ask Question Asked 8 months ago. Modified 8 months ago. Viewed ...
Comparing the cardinalities of infinite sets [duplicate]
2015年9月17日 · Comparing cardinalities between infinite sets. 1. Comparing the cardinalities of different sets.
Does the infinite series - Mathematics Stack Exchange
2019年12月27日 · If so, how would one go about showing this? I'm playing around with comparison proofs and wondering if theres a way to show this either diverges or converges (due to it's very close relation to 1/n). Would it be correct to say it diverges due to the fact that as n approaches infinity, the +1 becomes negligible?
0 or infinite limit in limit comparison test for improper integral
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