To prove that 2 is not a logical number, which method will be used: (a) with direct conclusion (b) discrete method (c) through counterexample (d) with opposite numbers?
Understand the Problem
The question is asking which method can be used to prove that the number 2 is not considered a logical number. The options given suggest different logical proof techniques.
Answer
With opposite numbers (proof by contradiction).
To prove that √2 is not a rational number, the method of proof by contradiction (option d: with opposite numbers) is typically used.
Answer for screen readers
To prove that √2 is not a rational number, the method of proof by contradiction (option d: with opposite numbers) is typically used.
More Information
The standard method to prove that √2 is irrational is to assume it is rational (can be expressed as a/b) and then show that this leads to a contradiction.
Tips
A common mistake is to confuse direct proof and proof by contradiction. The latter assumes the opposite of what needs to be proved and seeks a contradiction.
Sources
- Prove that Root 2 is Irrational Number - Cuemath - cuemath.com
- Mathematics Tools: Proof by Contradiction - .edc.org
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