How is it the 58th inauguration but only 45th president?

58th Inauguration means that there has been 58 scheduled ceremonies or transitions of power including George Washington first inauguration. [(2017-1789)/4] = 57+1 = 58.

Trump is 45th President because there have been 45 different changes of a person being named the presidency. He is only the 44th person to hold the presidential title because Grover Cleveland was elected after the 19th president (Arthur), then 21st president (Benjamin Harrison) was elected as the 21st president, then Cleveland was elected again so he is considered also the 22nd president.

But here is the math behind it - 58 scheduled inauguration - # of terms of presidents that had more than one term (21) + # of Extraordinary presidential shifts (9) - # of Non-Consecutive Presidents (1). = 58 - 21 + 9 - 1 = 45.