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
Alecsey [184]
3 years ago
9

Show that for any real number x ≥ 0 the set (x,x + 1]∩N is a singleton set

Mathematics
1 answer:
inessss [21]3 years ago
8 0

Answer: First, a singleton set is the set with only one element, for example, the set {∅} or set "null" is a singleton.

now, X ≥ 0, and X ∈ R.

(x,x + 1]∩N is the intersection between the set x and x+1 with the set of natural numbers, so the result of this operation is the set of all the natural numbers between x and x+1.

if x is a rational (or irrational) number, such as 1.5, then x +1 = 2.5

in (1.5, 2.5] there is only one natural element, the 2, then (x,x + 1]∩N is the singleton {2}

if x is a positive integer number, such as 1, then x + 1 = 2

the set is (1,2] is important to notice that 1 ∉ (1,2] because the set is open in the lower limit. so this set only contains one natural number, the 2; so again; the intersection with the natural set is a singleton

So this is proven for x rational, irrational and integers.

This happens because each element in the natural set is separated by the next one by 1, and in the set (x,x + 1]  although the distance between the lower and upper limits is 1, the set is open in the lower limit, so the distance is < 1. then you never can have two natural numbers on this set.

You might be interested in
A ferris wheel can accommodate 40 people in 30 minutes. How many people could ride the ferris wheel in 3 hours? What was that ra
andrew-mc [135]
240 people could ride it in 3 hours. The rate per hour is 80 people.


3 0
3 years ago
Suzannah made 7 bows. How many feet of ribbon did she use?
ella [17]

Answer:

420

Step-by-step explanation:

5 0
2 years ago
In 2007, there were more than 8.14 million cars for sale. Over the next 3 years, the number of cars decreased by 23%. Write an e
Nina [5.8K]

Answer:

c = 8.14 million×(0.9166)^t

4.83 million  

Step-by-step explanation:

Data:

  t = y - 2007

c₀ = 8.14 million

c₃  = 23 % less than c₁

Part 1. Calculate c₃

c₃ = c₀(1 - 0.23) = 0.77c₀

Part 2. Calculate r

      c₃ = c₀r^t

0.77c₀ = c₀r³

   0.77 = r³              Divided each side by c₀

         r = 0.9166     Took the cube root of each side

The explicit decay model is c = 8.14 million×(0.9166)^t

Part 3. Prediction

t = 2013 - 2007 = 6

c = c₀r^t = 8.14 million×(0.9166)⁶ = 8.14 million × 0.5929 = 4.83 million

The model predicts that there will be 4.83 million cars for sale in 2013.

7 0
2 years ago
Read the excerpt from act 1 of The Monsters Are Due on Maple Street.
Vika [28.1K]

Answer:

it is D. the murmurs of a group

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
The sum of the angle measures of a polygon with s sides is 2340. find s.​
marta [7]

Answer:

s = 15.

Step-by-step explanation:

The formula for a polygon with s sides is:

Sum of the angles = 180(s - 2) so we have:

180(s - 2) = 2340

180s - 360 = 2340

180s = 2700

s = 15

8 0
3 years ago
Other questions:
  • Jenny plans to have two children but doesn't know if they are boy-boy, girl-girl, or boy-girl. What is the probability that she
    10·2 answers
  • Daria walks 25 mile in 110 hour.
    9·1 answer
  • What is an equation of the line that is perpendicular to -x+2y=4 and passes through the point (-2, 1)
    6·1 answer
  • Find the y-intercept for the line represented by this equation. 3y+2x=-x+5
    9·1 answer
  • Which of the following statements is not always true? A. In a rhombus, both pairs of opposite sides are parallel. B. In a rhombu
    6·1 answer
  • Evaluate 0.53n+5 when n=3
    9·1 answer
  • 31. What is g(-2) for g(x) = 2x2 + 2x?<br> c. -<br> A. -2<br> B. -6<br> D. -3
    11·1 answer
  • Choose all true statements.
    12·2 answers
  • PLEASE I REALLY NEED HELP!! It is important during peer review to build onto another student's comments. Which comment builds be
    5·2 answers
  • HELPPPPPPPPPPPPPPPPPPPPPPP
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!