why is the below relation not a function?

radha

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If f is a function from set of all bit strings to the set of integers ,then


if we have a formal statement that f(s) is the smallest integer i such that ith bit of s is 1 and f(s)=0 when s is the empty string ,the string with no bits .


I am unable to get that why is this not a function.
 
If f is a function from set of all bit strings to the set of integers ,then


if we have a formal statement that f(s) is the smallest integer i such that ith bit of s is 1 and f(s)=0 when s is the empty string ,the string with no bits .


I am unable to get that why is this not a function.
Who said it wasn't a function? And why isn't it a function? Seems to me that, without trying to be too formal, a function is basically something that has only one output for a given input and your f(s) satisfies that. One could be more particular in your definition but I don't think it is necessary.
 
You start by saying "If f is a function" and then ask "why is f not a function?" That makes no sense!
 
If f is a function from set of all bit strings to the set of integers ,then if we have a formal statement that f(s) is the smallest integer i such that ith bit of s is 1 and f(s)=0 when s is the empty string ,the string with no bits . I am unable to get that why is this not a function.
I am not surprised at that because that statement is poorly stated.

The almost universal meaning of bit string in mathematics is a string of zeros and ones. If the question means something else by bit string it should say so.

Now, using the usual definition, the collection of all bit strings is uncountable (easily proven with a diagonal argument) therefore the collection cannot be listed. However, each string is a countable set of zeros and ones. So the function is well defined because the set of natural numbers is a well ordered set. Moreover, in any collection of bit strings there is at most one zero string (empty string); that string requires special attention.

Please post any more information you have about this question.
 
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