Determine whether the function 
given by mapping a real number 
to the first digit to the right of the decimal point in a decimal expansion of is well defined.
Recall that every real number which terminates in an infinite string of 0s has a second expansion which terminates in an infinite string of 9s. Any real number which terminates in an infinite string of 0s beginning in the first decimal place will be a counterexample to the functionhood of this relation. In particular, we have
and 
, but 
.
given by mapping a real number to the first digit to the right of the decimal point in a decimal expansion of is well defined.Recall that every real number which terminates in an infinite string of 0s has a second expansion which terminates in an infinite string of 9s. Any real number which terminates in an infinite string of 0s beginning in the first decimal place will be a counterexample to the functionhood of this relation. In particular, we have
and , but .
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