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Neporo4naja [7]
3 years ago
14

(1) In Section 1.4 we used the Axiom of Completeness (AoC) to prove the Archimedean Property of R (Theorem 1.4.2). Show that the

Monotone Convergence Theorem can also be used to prove the Archimedean Property without making any use of AoC.
(2) Use the Monotone Convergence Theorem to supply a proof for the Nested Interval Property (Theore 1.4.1) that doesn't make use of AoC. These two results suggest that we could have used the Monotone Con- vergence Theorem in place of AoC as our starting axiom for building a proper theory of the real numbers

Mathematics
1 answer:
serious [3.7K]3 years ago
3 0

Answer:

Both Answers are in the following attachment (a) and (b)

Step-by-step explanation:

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Simplify the expression: -3(x+6)
KATRIN_1 [288]

Answer:

-3x-18

Step-by-step explanation:

The expression -3(x+6) means that -3 is multiplied with x and 6 in the brackets so the answer would be

-3x-18

8 0
3 years ago
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X+4(2+3) < 5x is there a solution??
zavuch27 [327]

Answer:

\Huge\boxed{\mathsf{\longrightarrow X>5}}

Step-by-step explanation:

Isolate x on one side of the equation.

First, do parenthesis.

4(2+3)

Add.

3+2=5

Multiply.

4*5=20

Rewrite the equation problem.

x+20<5x

Secondly, subtract 20 from both sides.

x+20-20<5x-20

Solve.

x<5x-20

Thirdly, subtract 5x from both sides.

x-5x<5x-20-5x

Solve.

5-1=4

-4x<-20

Then, multiply -1 from both sides.

(-4x)(-1)>(-20)(-1)

Solve.

(-4x)(-1)=4x

(-20)(-1)=20

4x>20

Divide by 4 from both sides.

4x/4>20/4

Solve.

20/4=5

x>5

\Large\boxed{\mathsf{\Rightarrow X>5}}}

The solutions is 5, therefore, the correct answer is x>5.

5 0
4 years ago
What does 3(-1/4) equal
Kazeer [188]
The answer is -3/4 I got it on my calculator
5 0
3 years ago
Read 2 more answers
PLEASE HELP ASAP ASAP ASAP ASAP ASAPA ASAP
Shkiper50 [21]
5/3=1.6666 hope this helpssssssssssssssssssss
7 0
3 years ago
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charles is 22 years older than his sister danielle. in 10 years he will be twice as old as danielle. how old is each of them now
andriy [413]

9514 1404 393

Answer:

  • Charles: 34
  • Danielle: 12

Step-by-step explanation:

If Charles is 22 years older, he will be double Danielle's age when she is 22. If that is 10 years from now, Danielle is 12 and Charles is 34.

3 0
2 years ago
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