discrete test 2 Flashcards
set
unordered collection of elements shown as xEs
sets are equal
if and only if they have the same elements number and order do not matter
cardinality |s|
the number of elements of the set (repetitions dont add anything
a is a subset of b iff (sideways u greater than thing
every element of a is in b
P(a)
the power set is the set of all subsets.
Cartesian products
A x B (write it you bastard)
union aUb
set of all elements in a or b and both aUb
intersection anb
just things that are in both a and b
symmetric difference(+)
denoted a (+) b
a - b
everything in a that isnt in b
a-
everything not in a
domain of a function
input set
range of a funciton
output set
one to one
if no output values get mapped to any input values
onto
if every element of the output is mapped to some input
bijection
both one to one and onto
prove that it is a bijection
- prove one to one by setting equation equal to itself and canceling until x = x.
- prove that it is onto by solving for x separately in terms of y and plugging that in for x to get y = y
floor
round down
cieling
round up
geometric sequence
terms in a sequence can be found by multiplying by common number r
an = a0(r^n)
arithmetic sequences
terms in a sequence can be found by adding a common number d
an = a0 + (dn)
does it satisfy the recurrence relation
plug it in
find the sum of k as we go to n
n(n+1)/2
modular arithematic
a|b iff ak = b for some k
prime factorizations
make a tree of multiples down to primes
find the gcd
- get the prime factorization
2. get the smallest powers of the ones that they both share
find the lcm of each
take the larger power of each item. dont bother with repititons
