Formal proof Updated 2025-07-16
A proof in some system for the formalization of mathematics.
Lemma (mathematics) Updated 2025-07-16
A theorem that is not very important on its own, often an intermediate step to proving something that the author feels deserves the name "theorem".
Set (mathematics) Updated 2025-07-16
Intuitively: unordered container where all the values are unique, just like C++ std::set.
More precisely for set theory formalization of mathematics:
  • everything is a set, including the elements of sets
  • string manipulation wise:
    • {} is an empty set. The natural number 0 is defined as {} as well.
    • {{}} is a set that contains an empty set
    • {{}, {{}}} is a set that contains two sets: {} and {{}}
    • {{}, {}} is not well formed, because it contains {} twice
Function space Updated 2025-07-16
Most notable example: .
Number Updated 2025-07-16
Ordered pair Updated 2025-07-16
Sets are unordered, but we can use them to create ordered objects, which are of fundamental importance. Notably, they are used in the definition of functions.
Logic Updated 2025-07-16