tarzan2 (OP)
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May 02, 2015, 07:15:45 AM Last edit: May 21, 2015, 01:07:07 AM by tarzan2 |
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As the title claims.. first person to post correct solutions for all three problems will receive 0.1 btc. if someone submits correct answer for any 1 of the three they will receive 0.025 btc from me and 0.66 btc will remain on the remaining 2.. same idea if 2 are solved, such that the remaining problem will have a 0.33 bounty
i need the proof of proposition 6.7 as described here:
I need exercises 5 and 6 from here:
good luck!
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young3dvard
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May 02, 2015, 07:20:31 AM |
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you should use imgur and post the images here . using this paste the link of the image between
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polynesia
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May 02, 2015, 07:32:03 AM |
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For problem 5, does this work?
f(i,j)=(i−1)n+j
where i goes from 1 to m and j goes from 1 to n
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tarzan2 (OP)
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May 02, 2015, 07:39:16 AM |
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For problem 5, does this work?
f(i,j)=(i−1)n+j
where i goes from 1 to m and j goes from 1 to n
yea i think thats exactly right as a matter of fact.. could you just be a little more explicit for defining the bijection of m and n with respect to f(i,j)?
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polynesia
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May 02, 2015, 07:45:54 AM |
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For problem 5, does this work?
f(i,j)=(i−1)n+j
where i goes from 1 to m and j goes from 1 to n
yea i think thats exactly right as a matter of fact.. could you just be a little more explicit for defining the bijection of m and n with respect to f(i,j)? Thanks. Let me know a sample of the way you want to define the bijective function and I will help define it for you. My address: 1Nri6bYYB5jjVSQxum9jGkYNghqZHzUAfu
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tarzan2 (OP)
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May 02, 2015, 07:50:48 AM Last edit: May 21, 2015, 01:06:53 AM by tarzan2 |
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something like that i think would make the trolls happy.. i'm sending btc now
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polynesia
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May 02, 2015, 07:56:39 AM |
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tarzan2 (OP)
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May 02, 2015, 07:58:48 AM Last edit: June 24, 2018, 09:44:42 AM by tarzan2 |
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edit: hehe.. you think you could define the bijection? i am literally incapable of doing anymore math today. my brain is reeling
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polynesia
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May 02, 2015, 08:14:27 AM |
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0.025btc awarded to polynesia 97efdd32c3864b50ad56408830256a544689b576b18e8fe81eb7963fec4d78dc
edit: hehe.. you think you could define the bijection? i am literally incapable of doing anymore math today. my brain is reeling
Unfortunately, I don't get the notation required. Let me try to define it X = [m] x [n] Y = [mn] For each i (1<= i <= m) and j ( 1 <= j <= n), let us define a function f (i, j) such that f(i,j) = (i−1)n+j f is bijective from X to Y
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tarzan2 (OP)
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May 02, 2015, 08:16:30 AM |
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BEAUTIFUL
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polynesia
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May 02, 2015, 12:57:13 PM |
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Some small clarifications with respect to the first question
1) What is under your fingertips in the scanned image? 2) Does |-2-| indicate the set with just 2 elements {0,1}? 3) Is P(X) defined elsewhere?
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tarzan2 (OP)
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May 02, 2015, 01:03:00 PM |
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I'm glad your giving that one a shot because thats the real turd in the punchbowl.. so Y^X means the set of all functions with domain X and codomain Y. |2| notation thing is like you said, just {0,1}-so basically its talking about X->{0,1} for |2|^X P(X) is the power series of X, and it is what it is defined to be in the book.. i have a vague idea of what their talking about, the (xsi?-squiggly)X is the characteristic set of P(X) ie it is a set that defines where P(X) holds..
I hope this helps u squash this sucka
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polynesia
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May 03, 2015, 03:01:29 PM |
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Here goes my attempt at proposition 6.7
Proof that the function is injective Let F(S) = F(T) = A (which belongs to P(X))
Given the definition of F, we note that S is defined by S(x) = 1, for all x belongs to A S(x) = 0, for all x does not belong to A
We also note that since F(T) = A, T is defined by T(x) = 1, for all x belongs to A T(x) = 0, for all x does not belong to A
Since the definitions of S and T are identical, we conclude that S = T
Proof that the function is surjective Let A belong to P(X) Define the function J from X into |-2-| such that J (x) = 1, for all x belongs to A J (x) = 0, for all x does not belong to A
We note that F(J) = A, for any A Hence F is surjective.
Since F is injective and surjective, it is bijective.
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tarzan2 (OP)
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May 03, 2015, 03:26:01 PM |
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Nice! I think that could be it.. I'm sending coins now:) Get the last one and you'll get the full 0.1
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polynesia
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May 03, 2015, 04:14:31 PM |
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Nice! I think that could be it.. I'm sending coins now:) Get the last one and you'll get the full 0.1
Payment received. Thank you. Could you help me with the notation for the third question. What is Xe, Xo, Xi? Have they been defined elsewhere?
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tarzan2 (OP)
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May 03, 2015, 04:24:36 PM Last edit: May 21, 2015, 01:06:44 AM by tarzan2 |
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Yea.. I guess I thought it was a common definition Heres how they do it:
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tarzan2 (OP)
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May 03, 2015, 04:41:12 PM Last edit: May 21, 2015, 01:06:33 AM by tarzan2 |
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I think these pages are relevant as well :
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polynesia
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May 03, 2015, 11:34:52 PM |
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Thanks! That was helpful
(a) (5,0) - Xo (17,0) - Xo (18,0) - Xe
To check the solution, we can list down the antecedents of (5,0) (4,1), (3,0), (2,1), (1,0), (0,1) So (5,0) has 5 antecedents and our answer is correct.
So the element (x,0) can be defined to fall under Xe: x is even Xo: x is odd Xi is a null set
(b) Similarly (y,1) can be define to fall under Ye: y is even Yo: y is odd Yi is a null set
(c) The bijection is defined as F(x,0) = (x+1,1), if x is even F(x,0) = (x-1,1), if x is odd.
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TriggerX
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May 03, 2015, 11:44:56 PM |
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Has anyone solved it yet? If none, I could give it a shot.
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Hi!
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tarzan2 (OP)
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May 03, 2015, 11:48:24 PM |
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hmm... i think this is correct, but i'd need to spend more time to be sure... anyways its close enough if it isnt.. im sending polynesia the last of the bounty good job sir and thank you kindly Thanks! That was helpful
(a) (5,0) - Xo (17,0) - Xo (18,0) - Xe
To check the solution, we can list down the antecedents of (5,0) (4,1), (3,0), (2,1), (1,0), (0,1) So (5,0) has 5 antecedents and our answer is correct.
So the element (x,0) can be defined to fall under Xe: x is even Xo: x is odd Xi is a null set
(b) Similarly (y,1) can be define to fall under Ye: y is even Yo: y is odd Yi is a null set
(c) The bijection is defined as F(x,0) = (x+1,1), if x is even F(x,0) = (x-1,1), if x is odd.
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free bitcoin storage service! please send to: 1TArzAn26Wvw872Yw36JiBe21SEaypJTP
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