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Bijective function

Thu 10 May, 2012 11:54 pm
Let f be a bijective function defined on the set of non-negative integers {0,1,2...}, then is it possible that f (1) = 0 ?
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View best answer, chosen by uvosky
markr

1
Fri 11 May, 2012 09:01 am
@uvosky,
Sure. Here's one:

f(0) = 1
f(1) = 0
f(n) = n, for n > 1

1
Fri 11 May, 2012 10:02 am
@markr,

f(n) = n - 1
markr

1
Fri 11 May, 2012 05:30 pm
That maps 0 to -1, but the domain and range are non-negative integers.
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uvosky

1
Mon 14 May, 2012 05:51 am
@markr,
Actually, markr, the way you defined the function actually spoils the whole spirit of the question , because in your solution you directly use f ( 1) = 0 for defining the function , still it was a good approach.
markr

1
Mon 14 May, 2012 10:26 am
@uvosky,
I thought it was a question about existence. Perhaps you prefer this:

f(x) = x xor 1
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uvosky

1
Wed 23 May, 2012 12:21 am
I think I should modify the question I asked , one can of course have a bijective function defined on non-negative set of integers such that f ( 1 ) = 0 the fact that such a bijection exists is trivial ,
the question is to find an explicit formula for such a bijective function ;
and this one to markr , which xor operation are you using ? can you please be more specific .
markr

2
Wed 23 May, 2012 09:04 am
@uvosky,
bitwise exclusive or
Take the binary representation of the input and flip the least significant bit.
uvosky

1
Thu 24 May, 2012 12:24 am
@markr,
thanks
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