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Art [367]
3 years ago
5

HELP!! I will give 30 poins and brainliest to the one who gives me the right answer FIRST!!

Mathematics
1 answer:
KATRIN_1 [288]3 years ago
6 0

Answer:

What is the question

Step-by-step explanation:

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Let A be a finite, non-empty subset of R. Prove that A has a maximum and a minimum. (Recall that a maximum of a set A is an uppe
julia-pushkina [17]

Answer:

Let us use mathematical induction to prove the statement. So, we are going to start checking the statement for the first natural numbers.

n=1: Our set is \{x_1\}. So, obviously, x_1 is the maximum and minimum of our set. Then, the statement is true for n=1.

n=2: Our set is \{x_1,x_2\}. Necessarily, x_1 or x_1>x_2. In both cases, there is a minimum and a maximum.

Once we have our statement checked for the initial cases, we state our <em>induction hypothesis</em>:

For every finite set A of n elements there exists a maximum and a minimum.

Now, let us prove the that the above assertion is true for sets with n+1 elements.

Our set is A=\{x_1,x_2,\ldots,x_n,x_{n+1}\} and we want to find

\max\{x_1,x_2,\ldots,x_n,x_{n+1}\}.

Notice that this problem is equivalent to solve

\max\{\max\{x_1,x_2,\ldots,x_n\},x_{n+1}\},

i.e, to find the maximum among n+1 numbers, we can find first the miximum among n and then compare with the other one.

Now, using our induction hypothesis we know that there is a maximum in the set \{x_1,x_2,\ldots,x_n\}, because it has n elements. Let us write

x' =\max\{x_1,x_2,\ldots,x_n\}.

So, in order to find the maximum of A, we have to find the maximum of \A'={x',x_{n+1}\}. As we have checked at the beginning, there is a maximum in A', and it is the maximum of A.

Hence, we have completed the prove for the existence of the maximum of a set with n+1 elements. The prove for the existence of the minimum is analogue, we just need to change ‘‘maximum’’ for ‘‘minimum’’.

5 0
3 years ago
. Solve for the missing value.
choli [55]

Answer:

1. f= 9

2. y= 10

3. h= 2.5

4. q= 10

5. m= 6

Step-by-step explanation:

1. you divide both sides by 3 to get f by itself

2. you divide both sides with 6

3. you subtract because it is the opposite of addition. you could also write 5/2 but that’s not simplified enough

4. 10 x 4 = 40 so 10 is the answer

5. you subtract both sides by 6 and get 24. 24 divided by 4 equals 6

4 0
2 years ago
Read 2 more answers
What is the area of this face?​
Paladinen [302]

Answer:

242 ft^2

Step-by-step explanation:

15 x 14 + 4 x 8 = 242 ft^2

(break down the polygon into two rectangles)

6 0
3 years ago
Charles is doing renovations on his house. He has budgeted 25% of the cost for new
Rama09 [41]

Answer:

$14,400

<em>Brainliest, please!</em>

<em />

Step-by-step explanation:

25% is furniture, and furniture costs $3600.

So, 3600 x 4 is the total cost, which equals 14400

8 0
2 years ago
0.056 divided by -0.004
riadik2000 [5.3K]

Answer: -14

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
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