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
MariettaO [177]
1 year ago
12

Show that a discrete metric on a vector space X≠{0} cannot be obtained from a norm (the pair (X,d) is called the discrete metric

space if the metric is d(x,x)=0, d(x,y)=1 for x≠y).

Mathematics
1 answer:
topjm [15]1 year ago
4 0

You know that the discrete metric only takes values of 1 and 0. Now suppose it comes from some norm ||.||. Then for any α in the underlying field of your vector space and x,y∈X, you must have that

∥α(x−y)∥=|α|∥x−y∥.

But now ||x−y|| is a fixed number and I can make α arbitrarily large and consequently the discrete metric does not come from any norm on X.

Step-by-step explanation:

hope this helps

You might be interested in
Find the slope of the line through the given points. 1. (-4,-3) and (7, 1)​
Ostrovityanka [42]

Answer:

4/11

Step-by-step explanation:

We can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 1 - -3)/(7 - -4)

     = (1+3)/(7+4)

    = 4/11

8 0
2 years ago
Solve this system of linear equations. separate the x- and y- values with a coma. -12x=-75-11y
ycow [4]
Solve the following system:
{-12 x = -11 y - 75 | (equation 1)
{-5 x = -11 y - 89 | (equation 2)
Express the system in standard form:
{-(12 x) + 11 y = -75 | (equation 1)
{-(5 x) + 11 y = -89 | (equation 2)
Subtract 5/12 × (equation 1) from equation 2:
{-(12 x) + 11 y = -75 | (equation 1)
{0 x+(77 y)/12 = (-231)/4 | (equation 2)
Multiply equation 2 by 12/77:
{-(12 x) + 11 y = -75 | (equation 1)
{0 x+y = -9 | (equation 2)
Subtract 11 × (equation 2) from equation 1:
{-(12 x)+0 y = 24 | (equation 1)
{0 x+y = -9 | (equation 2)

Divide equation 1 by -12:
{x+0 y = -2 | (equation 1)
{0 x+y = -9 | (equation 2)
Collect results:
Answer:  {x = -2                {y = -9

please note that the parentheses "{" should span over both equations but the editor doesn't allow that so I should it on both line, See attached example.










4 0
3 years ago
X² - 4
emmainna [20.7K]
Yes so he shows this by also doing what is called the flow. After this it is complete
8 0
3 years ago
34+35
Musya8 [376]

you know dam well what 34+35 is...

70-1...

68+1....

aaaaaaaaand im gone bye

7 0
2 years ago
Read 2 more answers
34. Lora is thinking of a number. It is less than 50 It is a 2-digit number. 3 is a factor of this number. The sum of its digits
-Dominant- [34]

Answer:

B

Step-by-step explanation:

The number is between 10 and 49

The number is divisible by 3

Let the 10s digit = x

Let the units digit = y

1/3 * (10x + y)  = x + y          multiply both sides by 3

10x + y = 3(x +y)                  remove the brackets.

10x +y = 3x + 3y                  Subtract 3x from both sides

10x - 3x + y = 3y                  Combine\

7x + y = 3y                           Subtract y from both sides.

7x = 3y - y                           Combine

7x = 2y

x can't be very big. Even taking 1/3 will get out of range is you use 6.

Also x should be an even number. The units digit cannot have a fraction in it.

Try making x = 2

7*2 = 2*y

14 = 2y                                Divide by 2

14/2 = y

y = 7

So the number is possibly 27. Let's check it out.

  • The number is between and includes 10 and 49. 27 is between these two endpoints.
  • 27 is divisible by 3
  • 1/3(27) = sum of digits
  • 9 = (2 + 7)

All of the conditions are met. It's B

8 0
2 years ago
Other questions:
  • Sebastion swam laps every day in the community swimming pool. He swam 45 minutes each day, 5 days each week, for 12 weeks. In th
    8·1 answer
  • Ignore my work,I was just seeing if I know how to work the problem.​
    11·1 answer
  • Show all steps to solve:<br> 3( 1/6+2/9) + (-2)
    8·1 answer
  • What is the slope of the line that<br> passes through these two points?<br> (1, -2)<br> (3, 4)
    12·1 answer
  • 17+36=z-37 what is z
    5·1 answer
  • Michelle has 3
    10·1 answer
  • What is the volume, in cubic inches, of one cube with an edge length of inch?
    6·1 answer
  • To go to school in the morning. I first walk to the garden shed at 6 km/h to collect my bicycle. I then cycle to school at 15 km
    12·2 answers
  • #1: Find the value of X. (GEOMETRY)
    15·1 answer
  • I need help 1 through 13 please and thank you
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!