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
How many inches are equal to 13 feet?
iVinArrow [24]

Answer:

156

Step-by-step explanation:

1 foot = 12 inches

hope it helps

4 0
3 years ago
What does X equal in this problem
serg [7]

Answer: 98*

Alternate exterior angles are equal

8 0
3 years ago
Read 2 more answers
Imension
kipiarov [429]

Answer:

sorry can we have more info?

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Find the derivative of the given function at the indicated point f(x)=1/x a=2
soldi70 [24.7K]
For some unknown reason, Brainly won't post my answer as it assumes the answer has inappropriate words or a link.
So, I added the answer in the attached image.
Kindly check it.

7 0
3 years ago
Simplify this expression 10b+7-3b-2
iren2701 [21]

Answer:

7b+5

Step-by-step explanation:

10b + 7 − 3b −2

=10b + 7 + −3b + −2

Combine Like Terms:

=10b + <u>7 </u>+ −3b + <u>−2 </u>

=(10b + −3b) + ( <u>7 </u>+ <u>−2</u>)

=7b + <u>5</u>

Answer:

7b + 5

Hope this helps : )

3 0
3 years ago
Read 2 more answers
Other questions:
  • Quick Question. After dividing 30 by 2, do I multiply 15 by 3 or add 3 it to? (for question d) And thanks!
    10·2 answers
  • Please answer the following proof
    7·1 answer
  • 12 9/10 - 9 3/10...?...
    13·2 answers
  • ABC is similar to DEF. Find the length of
    8·1 answer
  • The area of the base of a right triangular prism is 9cm and the length of the prism is 10cm. Calculate the volume of the prism.
    5·1 answer
  • Mrs. diaz is thinking of buying an annual pass to Disneyland.
    12·2 answers
  • a parking lot is filled with 260 cars. 1/2 of the vehicles are suvs. 1/3 are sub compact cars. the rest are luxury cars. how man
    15·1 answer
  • What was the temperature at sea level at 20,000 ft
    8·1 answer
  • OK PLEASE HELP THIS IS DUE TONIGHT PLEASE HELPPPPP
    5·2 answers
  • To the nearest hundredth, 11.6/0.95 is about
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!