| It's been years that I haven't been here. Just come to announce several memoes:
1) New weblogs as follows:
http://sendoh.yculblog.com
http://sendoh.home.bj001.net
2) For RRR
How's everything? I don't know when you would see this message however, I will expect your reply anyway.
3) Fragments of the past
I don't want to make copies of the stuff loaded here and let it gone with the collapse of the system server. |
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| [Euler-Descarte's Formula]
---Proof.
Any connected map can be built up, edge by edge, from the primitive map that consists of a single isolated vertex. At each stage, the new edge either joins an ol d vertex to a new vertex, or joins two old vertices. In the former case, V and E are each increased by 1 while F is unchanged; in the latter, V is unchanged shile E and F are each increased by 1. In either case, the combination V -E + F is unchanged. The initial state we need is only one vertex and one region ( namely, one face), thus we have V -E + F=1-0+1=2. This value 2 is maintained throughout the whole construction. Thus, Euler's formula holds for every polyhedron built up from the initial object with one vertex and one face. |
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| [E-logic]
---Truth Functional Sentential Connectives.
SL9.3_Exercise
Question #5 Suppose there is a truth-functional sentential connective "#", and you are only told that "((P#P)#P)" is a tautology.
(a) What definite conclusions, if any, can you infer about the truth-table for the connective?
(b) How about the truth-value of "((Q&~Q)#(S&~S))"? Explain your reasoning clearly.
Answer #5 (Part a) "(P#P)" must be T and cannot be F when "P" is F. Why?
(Part b) T. Hint : What is the truth-value of an inconsistent WFF? |
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| [Macroeconomics]
---Lecture: ...
[French]
---Rivision of adjectifs and pays
[Concert]
---Manhattan Trio_Piano, Cello and Violin |
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