MAPPING VS FUNCTIONS
PAGE 1 OF 5, THE FUNCTION LAW
THE LAW
ONE INPUT, ONE OUTPUT
A function is a special kind of mapping: every allowed input must produce exactly one output. Think of a vending machine: press one button, you get one snack. Press the same button again, you still get one snack, not two different ones at once. A relation that sends one input to two different outputs breaks the law and is not a function. Many inputs may share the same output (that is fine), but one input can never split into two outputs. This single rule is the gatekeeper between casual "rules" and proper functions used in science, coding, and advanced maths.
⚡ THE FUNCTION LAW
Each input → exactly one output. One-to-many is NOT a function. Many-to-one IS still a function.
ONE!
VALID
✅ One arrow per input
📍 1 → 3 is fine
✅ Passes the function law
📍 1 → 3 is fine
✅ Passes the function law
INVALID
❌ 1 → 3 and 5
⚠️ Two outputs from one input
❌ NOT a function
⚠️ Two outputs from one input
❌ NOT a function