A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathmath333

  • one year ago

Set Theory

  • This Question is Closed
  1. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Let \(\large f\) be the subset of \(\large \mathbb{Z}\times \mathbb{Z}\) defined by \(\large f=\{(ab,a+b)\ ,a+b)\ :\ a,\ b \in \mathbb{Z}\}\) .Is \(\large f\) a function from \(\large \mathbb{Z}\) to \(\large \mathbb{Z}\) ?

  2. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    for f to be a function, what properties should f have?

  3. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    1 to 1 image

  4. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\large f=\{(ab,a+b)\ ,a+b)\ :\ a,\ b \in \mathbb{Z}\}\]Check if this is correct...

  5. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    correct

  6. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I think there's typo in (ab,a+b)

  7. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    1 Attachment
  8. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    ok ...

  9. hwyl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  10. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    0 maps to what?

  11. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\large {\text{Let} \quad f \ \text{be the subset of}\quad \mathbb{Z}\times \mathbb{Z} \\ \text{defined by} \quad f=\{(ab,a+b)\ :\ a,\ b \in \mathbb{Z}\} \\ .\text{Is}\quad f\ \text{ a function from} \ \ \mathbb{Z} \ \text{to}\ \mathbb{Z}} \)

  12. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    typo corrected

  13. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so, 0 maps to what in co domain?

  14. hwyl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1

  15. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i didnt understand ur question

  16. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1433162361384:dw|

  17. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    ok?

  18. hwyl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ab, a+b

  19. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    and many other values......

  20. hwyl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    a neq b where Z^+

  21. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    m still confuzed

  22. hwyl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    create a condition when it is not a one-to-one function

  23. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    by the definition of f, we can choose any a, b in integer set. So f will include ordered pairs: (0,1) when a=0 and b=1 (0,2) when a=0 and b=2 and so on.... So to be a function every x value should have a unique y value... So will f be a function?

  24. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no it has too many values to be unique.

  25. hwyl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you don't make any sense she clearly knows the definition of a function under what condition that (ab, a+b) is not a function when a,b are elements of Z

  26. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    You got it @mathmath333

  27. hwyl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if your domain is 0, clearly either a = 0 or b = 0 and one of them has to be greater than zero [(0*1), (0+1)] domain is 0, but the range is 1 and not 1 and 2

  28. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @hwyl I just show part of domain and codomain .. Not all elements...

  29. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    In fact they are infinite sets...

  30. hwyl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so when is it not a function?

  31. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so it is not a function ?

  32. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @amilapsn

  33. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you got... Do you want me to explain it little deeper?

  34. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no

  35. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    okay

  36. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.