Square-Sided Prisms are Countably Infinite
Jump to navigation
Jump to search
Theorem
There is a countably infinite different varieties of square-sided prisms.
Proof
By definition, a square-sided prism is made of:
- $2$ bases which are regular polygons
- as many lateral faces as there are sides of one of the bases.
Hence for each type of regular polygon there exists a corresponding square-sided prism.
There exists a type of regular polygon for each natural number greater than or equal to $3$.
There exists countably infinite set of natural numbers greater than or equal to $3$.
Hence the result.
$\blacksquare$