https://wiki.computability.org/ 2026-07-23T07:49:59+00:00 https://wiki.computability.org/ https://wiki.computability.org/lib/tpl/bootstrap3/images/favicon.ico text/html 2025-02-12T10:18:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.computability.org/topic:sets_sequences_reals?rev=1739355493&do=diff Sets of integers, binary sequences and real numbers In computability theory, there is a well-established tradition of identifying three distinct mathematical objects: sets of integers, infinite binary sequences, and real numbers. This identification is often useful, but it is important to recognize that the corresponding topological spaces are different and lead to distinct mathematical properties.\( A \subseteq \mathbb{N} \)\( n \)\( n \in A \)\( X \in 2^{\mathbb{N}} \)\( [0,1] \)\[ X = 0.X_0X…