Finite Simple Group of Order Two by The Klein Four Lyrics

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
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

Since 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 are 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 mirror pair, me and you
So let's apply forgetful functors to the past
And be a finite simple group, a finite simple group
Let's be a finite simple group of order two
(Oughter: "Why not three?")

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