Some light, coffee reading "Cardinality of the continuum" [1]: in short, the cardinality of real numbers (ℝ) is often called the cardinality of the continuum, and denoted by 𝔠 or 2^ℵ_0 or ℶ_1 (beth-one [2); whereas, interestingly [3], the cardinality of the integers (ℤ) is the same as the cardinality of the natural numbers (ℕ) and is ℵ_0 (aleph-null) [perhaps what was meant initially?].
Related: the Schröder–Bernstein theorem [4], "if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h : A → B.".
Not related, but great: Max Cooper (sound) and Martin Krzywinski (visuals) did a splendid job visualising "ℵ_2" [5].
[1] https://en.wikipedia.org/wiki/Cardinality_of_the_continuum
[2] https://en.wiktionary.org/wiki/%E2%84%B6
[3] "Cardinalities and Bijections - Showing the Natural Numbers and the Integers are the same size", https://www.youtube.com/watch?v=kuJwmvW96Zs
[4] https://en.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Bernstei...
[5] "Max Cooper - Aleph 2 (Official Video by Martin Krzywinski)", https://www.youtube.com/watch?v=tNYfqklRehM
Related: the Schröder–Bernstein theorem [4], "if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h : A → B.".
Not related, but great: Max Cooper (sound) and Martin Krzywinski (visuals) did a splendid job visualising "ℵ_2" [5].
[1] https://en.wikipedia.org/wiki/Cardinality_of_the_continuum
[2] https://en.wiktionary.org/wiki/%E2%84%B6
[3] "Cardinalities and Bijections - Showing the Natural Numbers and the Integers are the same size", https://www.youtube.com/watch?v=kuJwmvW96Zs
[4] https://en.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Bernstei...
[5] "Max Cooper - Aleph 2 (Official Video by Martin Krzywinski)", https://www.youtube.com/watch?v=tNYfqklRehM