Weird :S

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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).
 

Answers and Replies

  • #2
Tom Mattson
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What have you done so far?
 
  • #3
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Tom Mattson said:
What have you done so far?

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:
 
  • #4
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I'm surprised that nobody can solve this ......
 
  • #5
HallsofIvy
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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.
 
  • #6
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HallsofIvy said:
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.

[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:
  • #7
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Some of them are obvious...
 
  • #8
HallsofIvy
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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]
 
  • #9
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HallsofIvy said:
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]

So.. nr 6 is like.. 4, right?
 
  • #10
HallsofIvy
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Yes, that is correct- just count the number of symbols in the string.
 
  • #11
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aight, thanks for the help dude
 

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