Consistency (Meta) Math Example 3
Follow the full solution, then compare it with the other examples linked below.
Example 3
easyA proof assumes both ' is even' and ' is odd'. Is this assumption consistent? What follows?
Solution
- 1 A number cannot be both even and odd simultaneously ā the assumptions are inconsistent.
- 2 From a contradiction, any statement can be derived (ex falso quodlibet). The proof is therefore invalid unless this inconsistency was introduced deliberately as a proof by contradiction.
Answer
Inconsistent assumptions invalidate any argument built on them. In mathematics, the only legitimate use of contradictory assumptions is in proof by contradiction, where they are introduced to be refuted.
About Consistency (Meta)
The property of a set of mathematical statements having no internal contradictions ā all statements can be simultaneously true within the same system.
Learn more about Consistency (Meta) āMore Consistency (Meta) Examples
Example 1 easy
A student claims: 'The set [formula].' Check whether this definition is consistent.
Example 2 mediumCheck whether the system of equations [formula] and [formula] is consistent.
Example 4 mediumDetermine whether the conditions '[formula] is a prime number' and '[formula] is divisible by 4' are