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Step2247 [10]
3 years ago
13

What is wrong with the following proof that for every integer n, there is an integer k such that n < k < n + 2? Suppose n

is an arbitrary integer. Therefore k = n + 1.
a)Nothing.

b)The "therefore" phrase is illogical. The fact that n is an integer does not force us to define k as n + 1.

c)The proof writer mentally assumed the conclusion. He wrote "suppose n is an arbitrary integer", but was really thinking "suppose n is an arbitrary integer, and suppose that for this n, there exists an integer k that satisfies n < k < n+2." Under those assumptions, it follows indeed that k must be n + 1, which justifies the word "therefore": but of course assuming the conclusion destroyed the validity of the proof.

d)Since the theorem required the condition that k satisfies n < k < n + 2, a complete proof should at least mention that the chosen k satisfies that inequality, even if there is nothing to prove algebraically.
Mathematics
1 answer:
expeople1 [14]3 years ago
4 0

Answer:

c)The proof writer mentally assumed the conclusion. He wrote "suppose n is an arbitrary integer", but was really thinking "suppose n is an arbitrary integer, and suppose that for this n, there exists an integer k that satisfies n < k < n+2." Under those assumptions, it follows indeed that k must be n + 1, which justifies the word "therefore": but of course assuming the conclusion destroyed the validity of the proof.

Step-by-step explanation:

when we claim something as a hypothesis we can only conclude with therefore at the end of the proof. so assuming the conclusion nulify the proof from the beginning

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For a population with = 100 and = 20, what is the x value corresponding to z = 1.50?
mafiozo [28]

For a population with mean (μ) = 100 and standard deviation (σ) = 20, the X value corresponding to z = 1.50 is 130.

<h3>What is a z-score?</h3>

A z-score is also referred to as a standard score and it's a measure of the distance between a raw score and the mean, when standard deviation units are used.

<h3>How to determine the value of x?</h3>

In Statistics, the standardized z-score is giving by this formula:

Z=\frac{\bar{x}\;-\;\mu}{ \sigma }

Making x the subject of formula, we have:

x = Zσ + μ

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x = 1.50(20) + 100

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Read more on z-scores here: brainly.com/question/4302527

#SPJ4

Complete Question:

For a population with μ= 100 and σ = 20, what is the X value corresponding to z = 1.50?

30

101.5

115

130

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2 years ago
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