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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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The sum of two numbers is 24.The difference of their square is 144.what are the two numbers?​
dimulka [17.4K]

Answer:

9 and 16

Step-by-step explanation:

let the two numbers are X and Y

X+Y=24

X^2-Y^2=144

solve simultaneously

4 0
3 years ago
The slope of line m is 7/8. If n⊥m, what is the slope of line n?
Citrus2011 [14]
Hello!

Slopes of perpendicular lines are opposite reciprocals of each other, which the slope of line perpendicular to a line with a slope of 7/8 is -8/7.

Answer:
D. -8/7

Hope this helps!
8 0
3 years ago
Sarah,Leah,Haley and Kim bought 5 bottles of water to share among themselves. They divided each bottle of water into 4 equal por
Irina18 [472]

Answer:

Sarah have \frac{5}{4} bottle of water.

Step-by-step explanation:

We are given that,

Total number of bottles = 5

As, each bottle is divided into 4 portions.

The amount of water per person = \frac{1}{4}

Further, Sarah took 1 portion from each bottle and there are 5 bottles.

So, the amount of water Sarah have = \frac{1}{4}\times 5 = \frac{5}{4}

Hence, Sarah have \frac{5}{4} bottle of water.

5 0
2 years ago
A rug is 4 m wide. How much is this in centimeters?
Crank
It's very simple
1m=100cm
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6 0
3 years ago
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The absolute value is c.8

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