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Anton [14]
3 years ago
7

Consider the following proposed proof by contradiction that for all positive integers n, 3n > 2.

Mathematics
1 answer:
laila [671]3 years ago
7 0

Answer:

The proof contains a simple direct proof, wrapped inside the unnecessary logical packaging of a proof by contradiction framework.

Step-by-step explanation:

The proof is rigourous and well written, so we discard the second answer.

This is not a fake proof by contradiction: it does not have any logical fallacies (circular arguments) or additional assumptions, like, for example, the "proof" of "All the horses are the same color". It is factually correct, but it can be rewritten as a direct proof.

A meaningful proof by contradiction depends strongly on the assumption that the statement to prove is false. In this argument, we only this assumption once, thus it is innecessary. Other proofs by contradiction, like the proof of "The square root of 2 is irrational" or Euclid's proof of the infinitude of primes, develop a longer argument based on the new assumption, but this proof doesn't.

To rewrite this without the superfluous framework, erase the parts "Suppose that the statement is false" and "The fact that the statement is true contradicts the assumption that the statement is false. Thus, the assumption that the statement was false must have been false. Thus, the statement is true."

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Step-by-step explanation:

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Titus had 1/2 can of paint. He used 2/3 to paint a tabletop. What fraction of a full can of paint did Titus use?
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Determine the domain and range of the function f(x)= 3x+2. Also, state the intervals where the function f(x)= 3x+ 2 is increasin
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Answer:

Increasing on it's domain (-\infty,\infty) because the slope is positive.

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Step-by-step explanation:

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I should be able to plug in any number into 3x+2 and result in a number. There are no restrictions for x on 3x+2.

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Well y=3x+2 is a linear function that is increasing.  I know it is increasing because the slope is positive 3. I wrote out the positive part because that is the item you focus on in a linear equation to determine if is increasing or decreasing.

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