On Wikipedia (https://en.wikipedia.org/wiki/Dedekind_number), it is stated that the Dedekind’s number M(n) is the the number of abstract simplicial complexes with n elements.
This is incorrect, at least based on the Wikipedia definition of abstract simplicial complex, which does not allow the empty set as a face.
The correct definition is found in another Wikpedia site: https://en.wikipedia.org/wiki/Abstract_simplicial_complex
The number of abstract simplicial complexes on up to n elements is one less than the nth Dedekind number.
Mathtuition88 