[2015-05-10] Finite Simple Group of Order 2
0Originally recorded and posted to Facebook on 2015-05-10.
Here is a link to the original song that this is a cover of:
https://www.youtube.com/watch?v=BipvGD-LCjU
Original caption on Facebook:
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"Finite Simple Group of Order 2" by the Klein Four
The path of love is never smooth
But mine's continuous for you
You're the upper bound in the chains of my heart
You're my Axiom of Choice, you know it's true
But lately our relation's not so well-defined
And I just can't function without you
I'll prove my proposition and I'm sure you'll find
That we're a finite simple group of order two
I'm losing my identity
I'm getting tensor every day
And without loss of generality
I will assume that you feel the same way
'Cause every time I see you, you just quotient out
The faithful image that I map into
But when we're one-to-one you'll see what I'm about
'Cause we're a finite simple group of order two
Our equivalence was stable,
A principal love bundle sitting deep inside
But then you drove a wedge between our two-forms
Now everything is so complexified
When we first met, we simply connected
My heart was open but too dense
Our system was already directed
To have a finite limit, in some sense
I'm living in the kernel of a rank-one map
From my domain, its image looks so blue,
'Cause all I see is zeroes, it's a cruel trap
But we're a finite simple group of order two
I'm not the smoothest operator in my class,
But we're a dual pair, me and you,
So let's apply forgetful functors to the past
And be a finite simple group of order two
I've proved my proposition now, as you can see,
So let's both be associative and free
And by corollary, this shows you and I to be
Purely inseparable. Q.E.D.
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List of maths references:
path = https://en.wikipedia.org/wiki/Path_(topology)
smooth = https://en.wikipedia.org/wiki/Smooth_function
continuous = https://en.wikipedia.org/wiki/Continuous_function
upper bound = https://en.wikipedia.org/wiki/Upper_and_lower_bounds
chains = https://en.wikipedia.org/wiki/Total_order#Chains
axiom of choice = https://en.wikipedia.org/wiki/Axiom
- https://en.wikipedia.org/wiki/Axiom_of_choice
relation = https://en.wikipedia.org/wiki/Binary_relation
well-defined = https://en.wikipedia.org/wiki/Well-defined
function = https://en.wikipedia.org/wiki/Function_(mathematics)
proposition = https://en.wikipedia.org/wiki/Sentence_(logic)
finite simple group = https://en.wikipedia.org/wiki/Group_(mathematics)
- https://en.wikipedia.org/wiki/Simple_group
- https://en.wikipedia.org/wiki/Finite_group
order two = https://en.wikipedia.org/wiki/Order_(group_theory)
identity = https://en.wikipedia.org/wiki/Identity_element
tensor = https://en.wikipedia.org/wiki/Tensor
- https://en.wiktionary.org/wiki/tenser
without loss of generality = https://en.wikipedia.org/wiki/Without_loss_of_generality
quotient out = https://en.wikipedia.org/wiki/Quotient
faithful image = https://en.wikipedia.org/wiki/Image_(mathematics)
- https://en.wikipedia.org/wiki/Faithful_representation
map = https://en.wikipedia.org/wiki/Map_(mathematics)
one-to-one = https://en.wikipedia.org/wiki/Injective_function
equivalence was stable = http://mathworld.wolfram.com/StableEquivalence.html
principal love bundle = https://en.wikipedia.org/wiki/Vector_bundle
- https://en.wikipedia.org/wiki/Principal_bundle
wedge = https://en.wikipedia.org/wiki/Exterior_algebra
two-forms = https://en.wikipedia.org/wiki/Two-form
complexified = https://en.wikipedia.org/wiki/Complexification
simply connected = https://en.wikipedia.org/wiki/Simply_connected_space
open = https://en.wikipedia.org/wiki/Open_set
dense = https://en.wikipedia.org/wiki/Dense_set
system was already directed to have a finite limit = https://en.wikipedia.org/wiki/Direct_limit
kernel = https://en.wikipedia.org/wiki/Kernel#Mathematics
rank-one = https://en.wikipedia.org/wiki/Rank_(linear_algebra)
domain = https://en.wikipedia.org/wiki/Domain_of_a_function
zeroes = https://en.wikipedia.org/wiki/Zero_element
smoothest operator = https://en.wikipedia.org/wiki/Operator_(mathematics)
class = https://en.wikipedia.org/wiki/Class_(set_theory)
dual pair = https://en.wikipedia.org/wiki/Duality_(mathematics)
forgetful functors = https://en.wikipedia.org/wiki/Functor
- https://en.wikipedia.org/wiki/Forgetful_functor
associative = https://en.wikipedia.org/wiki/Associative_property
free = https://en.wikipedia.org/wiki/Free_object
corollary = https://en.wikipedia.org/wiki/Corollary
purely inseparable = https://en.wikipedia.org/wiki/Purely_inseparable_extension
Q.E.D = https://en.wikipedia.org/wiki/Q.E.D
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Full playlist:
https://www.youtube.com/playlist?list=PLr8zAQMT1EkphrHTiTemyqan9-ausbV4g