Special Cases
An exclamation mark indicates that one should compute the factorial of the term immediately to its left, before computing any of the lower-precedence operations, unless grouping symbols dictate otherwise. But 23! means (23)! = 8! = 40320 while 23! = 26 = 64; a factorial in an exponent applies to the exponent, while a factorial not in the exponent applies to the entire power.
If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus:
Sometimes a heavy dot is used as a multiplication sign which indicates that the entire expression before the heavy dot is multiplied by the entire expression after the heavy dot, but this notation may be misunderstood. Thus x + y • a + b may be used for (x + y)(a + b), but the latter notation is more common.
Read more about this topic: Order Of Operations
Famous quotes containing the words special and/or cases:
“History repeats itself, but the special call of an art which has passed away is never reproduced. It is as utterly gone out of the world as the song of a destroyed wild bird.”
—Joseph Conrad (1857–1924)
“The world men inhabit ... is rather bleak. It is a world full of doubt and confusion, where vulnerability must be hidden, not shared; where competition, not co-operation, is the order of the day; where men sacrifice the possibility of knowing their own children and sharing in their upbringing, for the sake of a job they may have chosen by chance, which may not suit them and which in many cases dominates their lives to the exclusion of much else.”
—Anna Ford (b. 1943)