1977 AHSME Problems/Problem 11
For each real number , let be the largest integer not exceeding (i.e., the integer such that ). Which of the following statements is (are) true?
Solution by e_power_pi_times_i
Notice that is just . We see that is true, as adding by one does not change the fraction part of the number. Similarly, is false, because does not always equal (If both numbers were , , ). Because is true and is false, the answer is .