Define proof by contradiction .

Proof by contradiction assumes the opposite of the result is true, then uses logical steps to show that this cannot be so.

What must you do at the start of a proof by contradiction?

Assume the opposite of what you are asked to prove, and state that assumption clearly.

True or False? A proof by contradiction can be written entirely in algebra, with no words.

False. It needs words alongside the algebra , both to state the assumption and to say clearly what has been shown.

What are two results that are standard set pieces for proof by contradiction?

Proving that a number is irrational , and proving that there are infinitely many primes .

What must you make clear at the end of a proof by contradiction?

Where the contradiction is . State what has been contradicted, then conclude that the original assumption must be false.

A LevelMathsEdexcelPureFlashcardsProofProof by Contradiction

Proof by Contradiction (Edexcel A Level Maths: Pure): Flashcards

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FrontProof by Contradiction
Define proof by contradiction.

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Cards in this collection (8)

Define proof by contradiction.
Proof by contradiction assumes the opposite of the result is true, then uses logical steps to show that this cannot be so.
What must you do at the start of a proof by contradiction?
Assume the opposite of what you are asked to prove, and state that assumption clearly.
A rational number can be written in the form $\frac{a}{b}$ , where $a$ and $b$ are $______$ with no common factors.
A rational number can be written in the form $\frac{a}{b}$ , where $a$ and $b$ are integers with no common factors.
When proving that a surd is irrational by contradiction, you begin by assuming it can be written as $\frac{a}{b}$ . Why must you state that $a$ and $b$ have no common factors?
Because the contradiction comes from later showing that $a$ and $b$ do share a factor. Without that condition there would be nothing to contradict.
True or False?
A proof by contradiction can be written entirely in algebra, with no words.
False.
It needs words alongside the algebra, both to state the assumption and to say clearly what has been shown.
What are two results that are standard set pieces for proof by contradiction?
Proving that a number is irrational, and proving that there are infinitely many primes.
Any composite number can be written as a product of $______$ .
Any composite number can be written as a product of primes.
For example, $28 = 2 \times 2 \times 7 = 2^{2} \times 7$ .
What must you make clear at the end of a proof by contradiction?
Where the contradiction is. State what has been contradicted, then conclude that the original assumption must be false.

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