Let N be the set of natural numbers and R the set of real nu

Let N be the set of natural numbers, and R the set of real numbers. Further, let aSmidgenLessThan be a relation between R and N such that for every ordered pair p aSmidgenLessThan, the second element is the least natural number that is greater than or equal to the first element. Is aSmidgenLessThan a function from R N? Why or why not?

Solution

It is not a relation.From the definition of a function we have\" A function is a set of ordered pairs in which each x-element has only ONE y-element associated with it\".but in the given relation we have infinitely many real numbers which give same natural number.

ex: if we take a real number 2.8 this gives you 3 which is nearest natural number to it. Same thing in case of 2.9 and 2.7 also.