23 янв. 2014 г. · The power set of any infinite set has greater cardinality. The power set of finite sets are also finite. Edit: I've been corrected on the ...

16 дек. 2019 г. · The cardinality of the real numbers (as the union of the rational and irrational numbers) can't be greater than that of the rational numbers.

28 авг. 2020 г. · Do sets with higher cardinality than the reals ( like 2^R), get endowed new useful properties, like we get when we go from N or Q to R?

5 мая 2022 г. · Despite the two points above, the real and complex numbers have the same cardinality, which you can think of as the number of elements. Upvote

25 июн. 2024 г. · In simple terms, if you have an infinite number of natural numbers, the set of real numbers is so huge that it can be thought of as having a ...

1 дек. 2015 г. · There are nonstandard models of the real numbers with cardinality greater than P(R). Also, take a look at the superstructure. Upvote 1

20 февр. 2019 г. · Yes you can. Let I be an infinite set. Consider the field F=Q(X_i| i in I) obtained by adjoining one transcendental variable to Q (the rationals) ...

28 июн. 2024 г. · The set of all functions from the real numbers to the real numbers has a larger cardinality than the set of real numbers.

23 мая 2022 г. · Real numbers comprise a"larger" infinity than natural numbers. But ... complex numbers useful, then they are the same "size" i.e. cardinality.

31 дек. 2023 г. · Another result from Cantor, Cantor's theorem, states that the cardinality of the power set of S is always greater than the cardinality of S.