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:
“Research shows clearly that parents who have modeled nurturant, reassuring responses to infants’ fears and distress by soothing words and stroking gentleness have toddlers who already can stroke a crying child’s hair. Toddlers whose special adults model kindliness will even pick up a cookie dropped from a peer’s high chair and return it to the crying peer rather than eat it themselves!”
—Alice Sterling Honig (20th century)
“To think is of itself to be useful; it is always and in all cases a striving toward God.”
—Victor Hugo (1802–1885)