1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
AlekseyPX
3 years ago
9

There is no smallest positive rational number because, if there were, then it could be divided by two to get a smaller one. EXPL

AINED
Mathematics
1 answer:
Gennadij [26K]3 years ago
3 0

Answer:

Since a/2⁽ⁿ ⁺ ¹⁾b <  a/2ⁿb,  we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.

Step-by-step explanation:

Let a/b be the rational number in its simplest form. If we divide a/b by 2, we get another rational number a/2b. a/2b < a/b. If we divide a/2b we have a/2b ÷ 2 = a/4b = a/2²b. So, for a given rational number a/b divided by 2, n times, we have our new number c = a/2ⁿb where n ≥ 1

Since \lim_{n \to \infty} \frac{a}{2^{n}b } = a/(2^∞)b = a/b × 1/∞ = a/b × 0 = 0, the sequence converges.

Now for each successive division by 2, a/2⁽ⁿ ⁺ ¹⁾b <  a/2ⁿb and

a/2⁽ⁿ ⁺ ¹⁾b/a/2ⁿb = 1/2, so the next number is always half the previous number.

So, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.

You might be interested in
Associations In Data:Question 10
Karo-lina-s [1.5K]

Answer:

\bar X = \frac{62+63+68+72+79+80+83+93+94+95}{10}= 78.9

|62-78.9| = 16.9

|63-78.9| = 15.9

|68-78.9| = 10.9

|72-78.9| = 6.9

|79-78.9| = 0.1

|80-78.9| = 1.1

|83-78.9| = 4.1

|93-78.9| = 14.1

|94-78.9| = 15.1

|95-78.9| = 16.1

MAD = \frac{\sum_{i=1}^n |X_i -\bar X|}{n}

And replacing we got:

MAD =\frac{16.9+15.9+10.9+6.9+0.1+1.1+4.1+14.1+15.1+16.1}{10}= 10.12

And the best anwer is

10.12

Step-by-step explanation:

We have the following data given:

62 63 68 72 79 80 83 93 94 95

And we need to begin finding the mean with the following formula:

\bar X = \frac{\sum_{i=1}^n X_i}{n}

And replacing we got:

\bar X = \frac{62+63+68+72+79+80+83+93+94+95}{10}= 78.9

Now we can find the mean absolute deviation like this:

|62-78.9| = 16.9

|63-78.9| = 15.9

|68-78.9| = 10.9

|72-78.9| = 6.9

|79-78.9| = 0.1

|80-78.9| = 1.1

|83-78.9| = 4.1

|93-78.9| = 14.1

|94-78.9| = 15.1

|95-78.9| = 16.1

And finally we can find the mean abslute deviation with the following formula:

MAD = \frac{\sum_{i=1}^n |X_i -\bar X|}{n}

And replacing we got:

MAD =\frac{16.9+15.9+10.9+6.9+0.1+1.1+4.1+14.1+15.1+16.1}{10}= 10.12

And the best anwer is

10.12

8 0
3 years ago
Use the drawing tool(s) to form the correct answer on the provided number line.
Nat2105 [25]

Answer:

j=42.36

Step-by-step explanation:

=15 to original answer

7 0
3 years ago
HELP WILLMARK BRAINLIEST.!!!!
navik [9.2K]
The answer is A i'm positive I used my caculater
6 0
3 years ago
What is the answer to this slope A (1,3),B (4,7)
jeyben [28]
The slope of these points is 4/3
7 0
3 years ago
Help on this question please. What is the perimeter of ABC?
mestny [16]

Answer:

Step-by-step explanation

5x2=10

3x2=6

2x2=4

the answer would be 20

8 0
3 years ago
Read 2 more answers
Other questions:
  • Is this a linear function?
    11·2 answers
  • How do you do 9/16x = 3/4
    7·2 answers
  • What does nPn represent?
    15·1 answer
  • Solve for<br> Give an exact answer.<br> 4(0.54 – 0.25) = 6+f
    5·1 answer
  • Factor.<br><br> x2−6x+8<br><br> Enter your answer in the boxes.
    11·2 answers
  • It takes 3/8 pound to fill one flower pot. Charlie has 5/6 pound of potting soil. How many pots can he dill
    9·1 answer
  • Can someone help me with this question
    10·1 answer
  • Given the sets above, select all (or the null set) of the element of: B
    6·1 answer
  • This is a simple probem
    12·1 answer
  • Lindsey rolled a six-sided number cube, labeled 1 through 6, twice. What is the probability that Lindsey rolled a number greater
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!