MHB Adjacency Matrix Problem and Alphabet Problem

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Could some please tell me if they think my answer for 1c and 3d of these questions I've done are right. thanks.View attachment 4393View attachment 4394
 

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These appear to be for credit. If so, it is against forum policy knowingly to help with such problems. Please PM if it is otherwise. Thread closed.
 

Thread 'Roulette wheel physics and probability'

Hi all, I've been a roulette player for more than 10 years (although I took time off here and there) and it's only now that I'm trying to understand the physics of the game. Basically my strategy in roulette is to divide the wheel roughly into two halves (let's call them A and B). My theory is that in roulette there will invariably be variance. In other words, if A comes up 5 times in a row, B will be due to come up soon. However I have been proven wrong many times, and I have seen some...
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Thread 'Detail of Diagonalization Lemma'

Thread 'Detail of Diagonalization Lemma'

The following is more or less taken from page 6 of C. Smorynski's "Self-Reference and Modal Logic". (Springer, 1985) (I couldn't get raised brackets to indicate codification (Gödel numbering), so I use a box. The overline is assigning a name. The detail I would like clarification on is in the second step in the last line, where we have an m-overlined, and we substitute the expression for m. Are we saying that the name of a coded term is the same as the coded term? Thanks in advance.
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