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How do I prove the statement p(n)= n >(or equal to) 0 using induction?
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[QUOTE="gopher_p, post: 4866648, member: 414293"] In part (a), you're meant to show that this function, ##\mathrm{Distance}(x,y)##, assigns a non-negative value to a pair of binary strings. In order to do that, you need to first understand the function. And in order to do that, you got to figure out what the algorithm is doing. The first tricky bit is understanding the meaning of the ##\oplus## operator. Your book tells you that this is meant to represent "exclusive or" but that's not really all that helpful. Basically, given ##a,b\in\{0,1\}##, ##a\oplus b=0## if ##a=b## and ##a\oplus b=1## if ##a\neq b##. Or to put it another way, ##a\oplus b=|a-b|##. Or to put it yet another way - a way that gets at the heart of the "exclusive or" business - ##a\oplus b=1## if and only if either ##a=1## or ##b=1##, but not both. Now given that, if I tell you that ##\mathrm{Distance}(x,y)=\sum\limits_{i=1}^n|x_i-y_i|##, can you figure out how the algorithm works? Note that this formula make the problem trivial, and completely doable without induction. So I give it only so that you may understand the algorithm. Also the ##p(n)## statement for part (a) would look something like, "If ##x## and ##y## are binary strings of length ##n##, then ##\mathrm{Distance}(x,y)\geq 0##." [/QUOTE]
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How do I prove the statement p(n)= n >(or equal to) 0 using induction?
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