What is the difference between “reductio ad absurdum” and “proof by contradiction”?

There is in mathematics a powerful method of proof known as “reductio ad absurdum” (Latin phrase: “reducing to absurdity”) or commonly referred to as “proof by contradiction”. Its reasoning is based on the fact that given a mathemati- cal statement S, either S is true or else not-S (negation of S) is true.

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What is reductio ad absurdum examples?

An example of reductio ad absurdum would be a an anti-Equal Rights advocate claiming that anyone in favor of an Equal Right Amendment must be in favor of killing babies. The reductio ad absurdum fallacy is similar to the straw person fallacy.

What is an example of proof by contradiction?

This, however, is impossible: 5/2 is a non-integer rational number, while k − 4j3 − 6j2 − 3j is an integer by the closure properties for integers. Therefore, it must be the case that our assumption that when n3 + 5 is odd then n is odd is false, so n must be even. This is an example of proof by contradiction.

What is the meaning of proof by contradiction?

To prove something by contradiction, we assume that what we want to prove is not true, and then show that the consequences of this are not possible. That is, the consequences contradict either what we have just assumed, or something we already know to be true (or, indeed, both) – we call this a contradiction.

What is another term for reductio ad absurdum?

In this page you can discover 4 synonyms, antonyms, idiomatic expressions, and related words for reductio ad absurdum, like: disproof, reduction, ridicule and reductio. Misinformation vs. Disinformation: A Simple Comparison.

What is the proof by reduction to absurdity?

Reductio ad absurdum is a Latin phrase which means “reduction to the absurd”. The phrase describes a kind of indirect proof. It is a proof by contradiction, and is a common form of argument. It shows that a statement is true because its denial leads to a contradiction, or a false or absurd result.

How is reductio ad absurdum used?

I see so that's reductio ad absurdum in a nutshell. It is reducing your opponent's argument to the absurd. By pushing the premises and conclusions to their logical limits or likewise strengthening

When should I use proof by contradiction?

1. Assume the opposite of your conclusion. …
2. Use the assumption to derive new consequences until one is the opposite of your premise. …
3. Conclude that the assumption must be false and that its opposite (your original conclusion) must be true.

What is the difference between proof by contradiction and proof by Contrapositive?

In a proof by contrapositive, we actually use a direct proof to prove the contrapositive of the original implication. In a proof by contradiction, we start with the supposition that the implication is false, and use this assumption to derive a contradiction. This would prove that the implication must be true.

One general reason to avoid proof by contradiction is the following. When you prove something by contradiction, all you learn is that the statement you wanted to prove is true. When you prove something directly, you learn every intermediate implication you had to prove along the way.

Is reductio ad absurdum a logical fallacy?

Sheldon: He’s engaging in reductio ad absurdum. It’s the logical fallacy of extending someone’s argument to ridiculous proportions and then criticizing the result.