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discrete Structures (cs 381, 361, 417), fibonacci sequence, demorgan'…

- - - - notation
        
        number types
        
        R
        
        set of all real numbers
        
        meaning
        
        the union of the set of all rational numbers with the set of all irrational numbers
        
        Z
        
        integers
        
        I
        
        imaginary numbers
        
        C
        
        complex numbers
        
        Q
        
        rational numbers
        
        N
        
        natural
        
        [ ]
        
        all real numbers between and including these numbers
        
        ( )
        
        all real numbers between but not including
        these numbers
        
        infinity is always non-inclusive because infinity is not a real number
        
        [ )
        
        all real numbers between these numbers, including the one on the left
        
        ( ]
        
        all real numbers between and these numbers, including the one on the right
        
        U
        
        union (of two sets)
    - - definition
        
        ordered set
      - types
        
        finite sequence
        
        infinite sequence
        
        arithmetic
        
        difference between terms can be expressed as
        
        {a, a+d, a+2d,....}
        
        a = first term
        
        d
        
        common difference
        
        terms can be found by adding/subtracting a constant
        
        geometric
        
        difference between terms can be expressed as
        
        {a, a(r), a(r^2),...}
        
        r
        
        common ratio
        
        terms can be found by multiplying/dividing a constant
      - pattern of a sequence
        
        3 step
        
        determine the simplest pattern
        
        put in terms of xn
        
        think of values that x can never be
        
        1/2,2/3,3/4,4/5,5/6,6/7,...
        
        xn = n/n+1
      - partial sum
        
        sum of any number of terms in a sequence
        but not all of them
    - - definition
        
        sum of all numbers in a sequence
      - types
        
        finite series
        
        infinite series
      - taylor series expansion
        
        optional
        
        remember: tristan taylor
      - maclaurin series exapansion
        
        optional:
        
        remember: kyle mclaughlin
    - - defintion
        
        collection of numbers
        
        notation
        
        { }
        
        set builder notation
        
        {type of number x | condition}