Set of Points on Line Segment is Infinite
Then there exists $n \in \N$ such that $S$ has $n$ elements.
Let $s_1$ and $s_2$ be two arbitrary adjacent points in $S$.
That is, such that there are no points in $S$ between $s_1$ and $s_2$.
Hence there must be more than $n$ elements of $S$.
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $1$: General Background: $\S 1$ What is infinity?