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
Which distance is about 3 x 10-5 meters?
tino4ka555 [31]

Answer:

I think that c is the correct answer

8 0
3 years ago
A taxi travels 25 km east of airport. Then it travels from that point to a point that is 40 km west of the airport. Finally the
Marizza181 [45]
The answer is:  " 95 km " .
__________________________________________________
Explanation:
__________________________________________________

                                   ("airport")
                                           •     {Step 1):       " 25 km east "               •<span>  
                                           </span>│===============================>  <span>│

                           </span>•  {Step 2):       " 40 km west ["of that point"] " ;        •                                             │<==========================================│<span>  
             
                          </span>•  {Step 3:  [back to airport] = " (40 km − 25 km) " ;

                                            • ("airport").
                         │=======>│
<span> _________________________________________________
                          
<u> Note</u>:  To find "total distance traveled:

" 40 km +</span> (40 km) + (40 km <span>− 25 km) " ; 

= </span>" 40 km + (40 km) + (15 km) " ;

= " 40 km + 40 km + (15 km) " ;

= 80 km + 15 km  ;   

=  95 km .
____________________________________________________
<span>
The answer is:  " 95 km <span>" .
</span>____________________________________________________

</span>
4 0
3 years ago
How many $0.21 pencils can be purchased for $7.00? Show your work.
IgorLugansk [536]
N*(21/100)=(700/100)

n=(700/100)/(21/100)

n=(700/100)*(100/21)

n=700/21

n=33+1/3

So <em><u>thirty three</u></em> $0.21 pencils can be purchased for $7.00.
8 0
3 years ago
Read 2 more answers
What is 0.984÷12.3? If you could show the work that would be awesome​
Stella [2.4K]

Answer:

0.08

Step-by-step explanation:

5 0
3 years ago
Is there a fast trick to convert centimeters to feet?
ElenaW [278]

Answer:

Step-by-step explanation:

The only way I know is to divide the centimeters by 30.48

4 0
2 years ago
Other questions:
  • Choice D is 100 plz help soon as possible
    12·1 answer
  • The point, (-4, 1) is located in which quadrant?
    7·1 answer
  • There are 6 quarters in a jar. Jill adds 2 quarters to the jar every day. Which linear equation represents the total amount of q
    13·2 answers
  • The average distance of the moon from earth is about 384,400 kilometers write this number in scientific notation
    12·1 answer
  • Which physical identity has the unit ms -square ?​
    9·1 answer
  • What is a one-step equation?
    6·1 answer
  • SOMEONE PLEASE HELP ME PLEASE
    8·2 answers
  • Mrs. Eng bought 4 packs of glue sticks. Each pack has 5 glue sticks. Her class uses 2 of the glue sticks for a project. How many
    13·1 answer
  • The table gives the amount of money (in dollars) spent on football by a major university. Letting 2 represent the number of year
    13·1 answer
  • A survey of birds in Forests A and B counted the number of robins and sparrows. Use the resulting frequency table to find each p
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!