1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Weird :S

  1. Mar 26, 2006 #1
    Let [tex]\Sigma[/tex] = {[tex] \beta[/tex],x,y,z} where [tex] \beta [/tex] denotes a blank, so x[tex]\beta \neq[/tex] x, [tex]\beta \beta \neq \beta[/tex], and x[tex]\beta[/tex]y [tex]\neq[/tex] xy but x [tex] \lambda[/tex]y = xy.

    Compute each of the following:

    1: [tex] \parallel \lambda \parallel [/tex]
    2: [tex] \parallel \lambda \lambda \parallel [/tex]
    3: [tex] \parallel \beta \parallel [/tex]
    4: [tex] \parallel \beta \beta \parallel [/tex]
    5: [tex] \parallel \beta[/tex]3 [tex] \parallel [/tex]
    6: [tex] \parallel[/tex] x [tex] \beta \beta [/tex] x [tex] \parallel [/tex]
    7: [tex] \parallel \beta \lambda \parallel [/tex]
    8: [tex] \parallel \lambda [/tex] 10 [tex] \parallel [/tex]

    Uhm.. can someone help me out ? :cry: I've tried like 3 days now (without progress).
  2. jcsd
  3. Mar 26, 2006 #2

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    What have you done so far?
  4. Mar 27, 2006 #3
    Well.. the problem is that i'm totally stuck. I have no idea what to do.. I've red the chapter over and over, checked several math websites, forum and so on.. :cry:

    It seems to me that people find it difficult to solve this no matter math skills :rolleyes:

    So if you don't want to help me (the assigment was handed in today).. that's ok. I can go on not understanding this.. :smile:
  5. Mar 29, 2006 #4
    I'm surprised that nobody can solve this ......
  6. Mar 29, 2006 #5


    User Avatar
    Science Advisor

    You haven't given a whole lot of information! You said [itex]\beta[/itex] represents a blank (I guess we might call that a "hard" blank) so really is treated just as another symbol. But what is [itex]\lambda[/itex]? The only thing you tell us about that is "but x[itex]\lambda[/itex]y= xy". So [itex]\lambda[/itex] is a "soft" blank- like nothing? Is [itex]\beta^3[/itex] the same as [itex]\beta\beta\beta[/itex]? And what, exactly is the definition of [itex]\parallel \parallel[/itex]? It would guess it is the length of the string but it would be a good idea to say that explicitely.
  7. Mar 29, 2006 #6
    [tex] \lambda [/tex] is according to definition a empty string - that is, the string consisting of no symbols taken from [tex]\Sigma[/tex].

    [tex] \{ \lambda \} \neq \emptyset [/tex] because [tex]| \{ \lambda \} | = [/tex] 1 [tex] \neq[/tex] 0 [tex] = | \emptyset | [/tex].

    [tex]\parallel [/tex] w [tex]\parallel[/itex] = the length of w, and [tex] \parallel \lambda \parallel [/tex] = 0. [tex]\parallel \beta \parallel [/tex] = 1. ...

    Sorry for the lack of information.. :frown:
    Last edited: Mar 29, 2006
  8. Mar 29, 2006 #7
    Some of them are obvious...
  9. Mar 29, 2006 #8


    User Avatar
    Science Advisor

    Indeed all of them are obvious. It's just counting!
    1.[tex] \parallel \lambda \parallel= 0 [/tex]

    2.[tex] \parallel \lambda \lambda\parallel= 0 [/tex]

    3.[tex] \parallel \beta \parallel= 1 [/tex]

    4.[tex] \parallel \beta^3= 3[/tex]

    8. [tex] \parallel \lambda^{10}= 0 [/tex]
  10. Apr 1, 2006 #9
    So.. nr 6 is like.. 4, right?
  11. Apr 1, 2006 #10


    User Avatar
    Science Advisor

    Yes, that is correct- just count the number of symbols in the string.
  12. Apr 1, 2006 #11
    aight, thanks for the help dude
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook