THEOREM: √2 is not a rational number

ASSUME: √2 is a rational number
i.e. √2 = X/Y where X, Y are integers with no common factors    (1)
      (cos by definition that what it means to be a rational number)

==> (√2)^2 = (X/Y)^2    (2)  (by squaring (^) each side)
==> 2 = X^2/Y^2    (3)  (by multiplying everything out)
==> 2Y^2 = X^2    (4)  (by multiplying both sides by Y^2)
==> X^2 = 2Y^2    (5)  (by reversing the equation)
==> X^2 is even    (6)  (cos 2 times anything is even)
==> X is even    (7)  (cos if X it were odd, X^2 would be odd)
==> X = 2P where P is some other positive integer     (8)
       (cos by definition that’s what it means for X to be even)
(4) and (8) ==> 2Y^2 = (2P)^2    (9)  (by substituting for X)
==> 2Y^2 = 4P^2    (10)  (by multiplying everything out)
==> Y^2 = 2P^2    (11)  (by dividing both sides by 2)
==> Y^2 is even    (12)  (cos 2 times anything is even)
==> Y is even    (13)  (cos if Y it were odd, Y^2 would be odd)
==> Y = 2Q where Q is some other positive integer     (14)
       (cos by definition that’s what it means for Y to be even)
(1), (8) and (14) ==> X/Y = 2P/2Q  (17)  (by substituting for X and Y)
==> X and Y have a common factor of 2  (18)  (cos we can see the 2’s)
==> The assumption at (1) is false  (19)
       (cos it says: “X, Y are integers with no common factors”)
==> √2 is NOT rational 
Q.E.D


POETRY!

the movement of a whirlpool
draining the oceans i filled for you
each drop a thought, i shed for you
cannot stop, i depend on you
it is stupid, it is a ruse
to paint you as my muse
but my heart is wicked and bruised
i channel the purple and blue hues
i wait for the time to be used
produce fruits for a love that never took root

What becomes of the handful of leaves from
the young tree which is sawed off at the root?

cityscapes and heartbreaks
808s and carrot cakes
my life took a turn, a left
you tried to make me burn but I left
you at the alter, my destiny I cannot falter
I let me get softer, left the slaughter
watercolour paints and growing pains
deep introspection and soaking rains
get to the root of the issue, the root of the pain
elevate, activate
popping off like champagne

jealousy is the root of evil
once said, there is no retrieval

jealousy is the root of evil,
once felt, there is no retrieval.