What you’ll learn
Formal function definition.
Key idea
The defining restriction is one output per input, not one input per output.
Each individual pair having one output does not establish uniqueness across repeated inputs; injectivity is not required.
Worked example
Classify examples and non-examples for the concept 'Formal function definition'.
Classify relation {(1,-2),(1,0),(2,-2)} from x input to y output using the function definition.
- Group ordered pairs by first coordinate; the function condition is uniqueness of output for each input.
- input 1 has two distinct outputs -2 and 0.
Answer: Not a function — input 1 has two distinct outputs -2 and 0.
Quick Check
Classify examples and non-examples for the concept 'Formal function definition'.
Classify relation {(1,2),(2,5),(3,2)} from x input to y output using the function definition.