Finite Simple Group (of Order Two)

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Finite Simple Group (of Order Two)
The Klein Four Group

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.

Channel: Music
Uploaded: April 14, 2006 at 2:10 am
Author: oneofvipper

Length: 00:03:03
Rating: 4.89
Views: 405819

Tags: Finite Simple Group of Order Two The Klein Four Math

Video Comments:
thoughtheglass (December 27, 2008 at 11:47 am)
if the path of love is (never smooth on a given interval)oe as to wonder what mapings would make it continuos for you
thepathofglorylead (December 25, 2008 at 3:19 am)
Great! What about hte original's name?
seu754e5rjdjf7 (December 23, 2008 at 1:23 am)
No no, he said he was a PhD student at STANFORD, that's believable-- I pretty much expected him to miss *all* of the references.
seu754e5rjdjf7 (December 23, 2008 at 1:18 am)
If he loses his partner, they're no longer a group of order 2, irrespective of who represents the identity element. I would assume the singer is the identity element, not that the girl is the identity element and that he's implying he's losing his lover by "losing his identity".
seu754e5rjdjf7 (December 23, 2008 at 1:07 am)
Pretty sure "order" meaning cardinality is fine. Group of order 2-- cardniality being the number of elements-- and there's two elements (people) in the group (relationship). Sorry if I'm mistaken, but I don't get where you're coming up with "order four".
ldb579932 (December 23, 2008 at 7:11 am)
If the singer is the identity element then they may not have a good love life as he would be idempotent.
ldb579932 (December 23, 2008 at 7:18 am)
Multiple math meanings of order: order of a group means cardinality, order of an element means least repeated operations to get identity, and order as in a1<a2<a3...
manueljesusarredondo (December 27, 2008 at 3:31 pm)
the description of the video mentions we are talking about The Klein Four Group which has cardinality four
AlephHaz (December 29, 2008 at 6:55 am)
That's the name of the group that's singing.

In the song, they're mentioning a totally different mathematical group.

I believe order in this context is the cardinality of the set in the group.
seu754e5rjdjf7 (December 23, 2008 at 1:02 am)
Pretty sure I disagree-- linear & abstract algebra, topology, etc... pretty sure you don't need any of that to teach high school math.