Completeness (Intuition) Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
A student proves a statement for all even integers but forgets odd integers. Is the proof complete? What is missing?

Solution

  1. 1
    No ā€” the proof is incomplete. It only covers even integers.
  2. 2
    To be complete, the argument must also handle all odd integers (or show the statement holds for all integers together).

Answer

IncompleteĀ ā€”Ā oddĀ integersĀ areĀ notĀ covered\text{Incomplete ā€” odd integers are not covered}
Completeness in a proof means every case in the claimed domain is addressed. Covering only a subset of cases leaves the proof incomplete, no matter how correct the covered portion is.

About Completeness (Intuition)

The property of a mathematical system where every true statement that can be expressed in the system can also be proved within it.

Learn more about Completeness (Intuition) ā†’

More Completeness (Intuition) Examples

Example 1 easy

The real numbers [formula] are 'complete' while the rationals [formula] are not. Illustrate this by

Example 2 medium

Check that a proof by induction for [formula] is complete: what cases must be covered? Use [formula]

Example 4 medium

State whether [formula] or [formula] is a better domain for solving [formula], and explain in terms

ā† All Completeness (Intuition) Examples Completeness (Intuition) Concept

Related Concepts

Consistency (Meta)