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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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Please help, I have two questions that I need answers to for 25 points!
arsen [322]

Answer:

1) 6+7=42feet^{2}

2) Beginning (0,0,-25) end (0,-20,-25)  

Step-by-step explanation:

1) Plot these point on graph. By this you can determine the fourth coordinate(-3,4) as it is a rectangle.

So, length =7

     breadth =6

area =7*6 =42feet^{2}

2) Here height of rack is 25 feet thus it's Z coordinate is -25.

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7 0
3 years ago
Find the fifth term of a sequence whose first term is 8 and common ratio is 3/2
Arlecino [84]

Answer:

Option c. 81/2

Step-by-step explanation:

Fifth term: a5=?

First term: a1=8

Common ratio: r=3/2

an=a1*r^(n-1)

with n=5

a5=a1*r^(5-1)

a5=a1*r^4

Replacing the known values:

a5=8*(3/2)^4

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Answer: Option c. 81/2

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geniusboy [140]
6 Cucumbers = $2
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12 peppers= $9
$9/12= $0.75 per pepper
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$4/6= $0.66 per tomatoes
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18 peppers= $13.5
21 tomatoes=$13.86
Total= (2.97+13.5+13.86)----> $30.33



3 0
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