In type theory and some fields of logic, 2 is usually defined as (λf.λx.f (f x)); essentially, the concept of doing something twice.
That's the number of all directed graphs, some of which certainly have cycles.
Surveyed. Looking forward to the data and analysis, as per every year.
That's not how Big O notation works: O(100,000) = O(1).
You presumably mean "in the order of 100,000", which is sometimes written "~100,000".
This is at least as old as Leibnitz.