Introduction to Set Theory by Hrbacek Karel; Jech Thomas; & Thomas Jech

Author:Hrbacek, Karel; Jech, Thomas; & Thomas Jech
Language: eng
Format: epub
Publisher: CRC Press LLC
Published: 2017-02-14T16:00:00+00:00

1.8 Corollary*

The set of all real numbers is not the union of countably many countable sets.

Proof. The set R is uncountable.

1.9 Corollary*

The ordinal ω1 is not the supremum of a countable set of countable ordinals.

Proof. If {αn | n ∊ N} is a set of countable ordinals, then its supremum

is a countable set, and hence α < ω1.

1.10 Theorem *

2No ≥ N1.

Proof This follows from Theorem 1.5 and the fact that 2No ≥ N0.

As a result, the Continuum Hypothesis can be reformulated as a conjecture that

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.