Add factors:
1+2+3+4+6= 16
16 12
≠
Add factors:
1+2+3= 6
6=6
***6 is a perfect number
6
C
B
A
1
1
1
a
Every rational number has a decimal expansion with a repeating pattern of digits.
Irrational numbers have no pa
**Odds square to odd numbers and evens square to even numbers.
Irrational numbers guarantee no repetitions
Elements of the sets (members)
N= Natural Numbers, whole numbers
Q= Rational Numbers, can be written as a ratio
= subset
ε
= membership
{ } = set
U = union
∩
= intersection
U
= universal set
# = number
First element
Second element
Third element
Fourth element
all positive fraction
(Rational numbers)
covered by this scheme.
First element
Second element
Third element
Fourth element
Fifth element
Sixth element
Exterior angle
Interior angle
Pan
(2,1)
(1,0)
(0,0)
(1,1)
(0,1)
(x
1
,x
2
)
0 1 0 1
Totally there are four possibilities
4 vertices
(1,0,1)
(1,0,0)
(0,0,0)
(1,1,0)
(1,1,1)
(0,1,1)
(0,0,1)
(0,1,0)
(3,4)
3
(3,1)
(1,2)
Real Numbers
Imaginary Numbers
January 22, 2008
Numbers –
1, 2,3,4,5 … (natural numbers)


pattern
Spotting Patterns
1.
2,4,6,8…
(even numbers)
2.
2,4,8,16,32…
(powers of 2)
3.
2, 3,5,7,11,13…
(prime numbers)
4.
1, 1,2,3,5,8,13…
(Fibonacci Numbers – adding two previous numbers to get the next)
Prime Numbers
Prime Numbers
are only divisible by 1 and itself ex. 5 is a prime number but 6 is not.
1.
Compare
Even – 2, 4, 6,8,10…
Prime – 2,3,5,7,11,13,17.19,23,29…
*Primes cannot be predicted they must all be figured out.
No known formula.
No easy way to tell if a number is prime.
2.
Goldbach’s conjecture (“guess”)
Every even number greater than 2 is the sum of two primes
12=5+7
32=13+19
32=3+29
3.
How many primes?
2,3,5,7,11,13,17,19,23,29,31,37,41,43…
There are infinitely many.
4.
Twin primes
Successive odd numbers that are prime