![subject](/tpl/images/cats/mat.png)
Mathematics, 11.02.2020 21:46 jessiegarrison1
Identify all mistakes made in the following proof that for each integer n, there is an integer k such that n < k < n+2.
Suppose n is an arbitrary integer. Therefore, k = n + 1 for all integers n. This means that n < n + 1 < n + 2. This proves that an integer k exists.
ASuppose n is an arbitrary integer. Therefore, k = n + 1
The choice of k = n + 1 does not follow from the fact that n is an integer. The inappropriate word "Therefore" should be replaced by "Pick", "Select", "Choose" or other words to that effect.
BTherefore, k = n + 1 for all integers n.
After we decided that n is some integer, n is just that - an integer. It's no longer a free variable. It makes no sense to apply universal quantification to it, again just like it makes no sense to say " 2 + 3 = 5 for all integers 5".
CTherefore, k = n + 1 for all integers n. This means that n < n + 1 < n + 2.
It makes no sense to draw a conclusion from a variable definition that does not reference the variable. n < n + 1 < n + 2 is true for all n regardless of what k is. The proper conclusion to be drawn from the definition of k is that n < k < n+2.
D This proves that an integer k exists.
We know that integers exist. If we're going to make a concluding statement that summarizes the theorem we have proved, we must quote the theorem correctly, not a caricature of our theorem. A correct concluding statement would be: this proves that for every integer n, an integer k exists such that n < k < n+2.
![ansver](/tpl/images/cats/User.png)
Answers: 2
![](/tpl/images/ask_question.png)
![](/tpl/images/ask_question_mob.png)
Another question on Mathematics
![question](/tpl/images/cats/mat.png)
Mathematics, 21.06.2019 15:30
Which conjunction is disjunction is equivalent to the given absolute value inequality? |x+2|< 18
Answers: 1
![question](/tpl/images/cats/mat.png)
Mathematics, 21.06.2019 16:50
If the table of the function contains exactly two potential turning points, one with an input value of β1, which statement best describes all possible values of m? m β₯ β12 β12 < m < 4 m β€ 4 m β₯ 4 or m β€ β12
Answers: 1
![question](/tpl/images/cats/mat.png)
Mathematics, 21.06.2019 18:00
Find the number of liters in 12.8 gal of gasoline. round to the nearest hundredths
Answers: 2
![question](/tpl/images/cats/mat.png)
Mathematics, 21.06.2019 19:40
The owners of four companies competing for a contract are shown in the table below. if a report is released that advocates company b, which of the people having funded the report should result in the most skepticism? company owner of company company a jake adams company b company c company d debby smith henry rose rhonda baker o a. jake adams o b. rhonda baker o c. debby smith o d. henry rose
Answers: 2
You know the right answer?
Identify all mistakes made in the following proof that for each integer n, there is an integer k suc...
Questions
![question](/tpl/images/cats/mat.png)
![question](/tpl/images/cats/istoriya.png)
History, 16.02.2020 23:05
![question](/tpl/images/cats/mat.png)
Mathematics, 16.02.2020 23:05
![question](/tpl/images/cats/mat.png)
Mathematics, 16.02.2020 23:05
![question](/tpl/images/cats/biologiya.png)
Biology, 16.02.2020 23:05
![question](/tpl/images/cats/mat.png)
Mathematics, 16.02.2020 23:05
![question](/tpl/images/cats/mat.png)
Mathematics, 16.02.2020 23:06
![question](/tpl/images/cats/istoriya.png)
History, 16.02.2020 23:06
![question](/tpl/images/cats/mat.png)
![question](/tpl/images/cats/fizika.png)
![question](/tpl/images/cats/mat.png)
Mathematics, 16.02.2020 23:07
![question](/tpl/images/cats/mat.png)
![question](/tpl/images/cats/himiya.png)
![question](/tpl/images/cats/geografiya.png)
![question](/tpl/images/cats/himiya.png)
![question](/tpl/images/cats/mat.png)
![question](/tpl/images/cats/mat.png)
Mathematics, 16.02.2020 23:09
![question](/tpl/images/cats/mat.png)
![question](/tpl/images/cats/en.png)
English, 16.02.2020 23:10