Differentiation Between Math Notes

• Definition/Example, either of an object or of a notion, which links to:

• Types: Objects/notions of type object/notion with additional restrictions.

• Examples: Specific examples or counterexamples of object/notion (but not of any of its types).

• Constructions: Objects/notions derived from object/notion.

• Generalizations: Abstractions of object/notion.

• Properties: Statements regarding object or necessary conditions of notion.

• Sufficiencies: Proofs that other objects are of type object or sufficient conditions of notion

• Equivalences: Equivalent definitions for object or biconditionals between notions and notion.

• Justifications: Proofs of well-definition of object/notion.

• Proposition/Theorem (differentiated by ‘importance’), including both statement and proof regarding object/notion, which links to:

• Proved by: Statements in which proof depends crucially on.

• References: Notes in which the proofs of statement (or corollaries thereof) are delegated to.

• Justifications: Proofs of implicit assumptions of object/notion in statement.

• Specializations: Reformulations/proofs of instances of statement.

• Generalizations: Statements and proofs of abstractions of statement.