The setting for formal logic

• Three components:
• A mathematical entity of interest
• For example: Complex numbers, real-valued functions, vector spaces, etc.
• A set of “strings”
• defined syntax
• Algorithmically comprehensible
• “starter” strings (“axioms”)
• Rules for combining strings to create new ones (“rules of inference”)
• A mapping between the two
• Manipulate the strings, perhaps algorithmically, to reason about the mathematical object