query: Three kinds of infinities
positive_passages.docid: 27290
positive_passages.text: What Does it Really Mean to Have Different Kinds of Infinities?
negative_passages.docid: 94433
negative_passages.text: Rigorous underpinnings of infinitesimals in physics
negative_passages.docid: 112910
negative_passages.text: Is the set of real numbers really uncountably infinite?
negative_passages.docid: 94055
negative_passages.text: Extending Rolle's Theorem to Infinity
negative_passages.docid: 70940
negative_passages.text: Homework - set theory infinite union
negative_passages.docid: 24924
negative_passages.text: Computing an infinite product
negative_passages.docid: 52451
negative_passages.text: Ordered Triples and Set Theory
negative_passages.docid: 132537
negative_passages.text: Class of sets of a given infinite cardinality
negative_passages.docid: 87356
negative_passages.text: Are there any known uncountable transfinite increasing sequences of real numbers?
negative_passages.docid: 154796
negative_passages.text: Completeness of sequence of reals with finitely many nonzero terms
negative_passages.docid: 112899
negative_passages.text: Final theory in Physics: a mathematical existence proof?
negative_passages.docid: 55619
negative_passages.text: What does $\bigcup_{i=0}^{\infty}[i, i+2]$ mean?
negative_passages.docid: 79389
negative_passages.text: Is there an intuitionist (i.e., constructive) proof of the infinitude of primes?
negative_passages.docid: 72007
negative_passages.text: What do finite, infinite, countable, not countable, countably infinite mean?
negative_passages.docid: 65473
negative_passages.text: How can something finite become infinite?
negative_passages.docid: 50584
negative_passages.text: Parallel universes: are there an infinite amount of universes?
negative_passages.docid: 9651
negative_passages.text: Cardinality of cartesian product of an infinite set with N