Honors Pre-Calculus
... • A numerical set is said to be closed under a given operation if when that operation is performed on any element in the set the result of that operation is in that set. • For example {x|x is even} is closed under addition because an even number plus an even number is even. • {x|x is odd} is not clo ...
... • A numerical set is said to be closed under a given operation if when that operation is performed on any element in the set the result of that operation is in that set. • For example {x|x is even} is closed under addition because an even number plus an even number is even. • {x|x is odd} is not clo ...
![[Part 3]](http://s1.studyres.com/store/data/008795885_1-d87cc86e59aaf2f47366e1db501c3b95-300x300.png)
A 1 ∪A 2 ∪…∪A n |=|A 1 |+|A 2 |+…+|A n
... Proof:In constructing an r-permutation of an nelement set, we can choose the first item in n ways, the second item in n-1 ways whatever choice of the first item,… , and the rth item in n-(r-1) ways whatever choice of the first r-1 items. By the multiplication principle the r items can be chosen in ...
... Proof:In constructing an r-permutation of an nelement set, we can choose the first item in n ways, the second item in n-1 ways whatever choice of the first item,… , and the rth item in n-(r-1) ways whatever choice of the first r-1 items. By the multiplication principle the r items can be chosen in ...
COMPLEX NUMBERS
... There is no real number x satisfying the equation x 2 = −1. A solution can be obtained by introducing a new number i which is assumed to satisfy i 2 = −1. A complex number is then one of the form a + ib where a and b are real numbers. Complex numbers are compared for equality, added and multiplied u ...
... There is no real number x satisfying the equation x 2 = −1. A solution can be obtained by introducing a new number i which is assumed to satisfy i 2 = −1. A complex number is then one of the form a + ib where a and b are real numbers. Complex numbers are compared for equality, added and multiplied u ...
