Htam::Etc.Klein4

The Klein Four Group is an a capella group of math nerds.
At Caltech these days, a lot of people have been listening to Finite Simple Group of Order Two. It is a very good song. The lyrics is as follows with links to Mathworld of math terms I happened to recognize. If you see more math terminology or mis-interpreted links (some math terms have very many completely different meanings) let me know.

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.

Other terms.

Without loss of generality. In proofs, we often like to be as succinct as possible. The phrase speak for it self. For instance, we might use WLOG when describing groups of order p q, where p and q are distinct primes. We may say, ``without loss of generality, assume p > q.
Assume. We say `assume' when we have a right to assume something not given: WLOG as above or when all other cases have been exhausted. We say `suppose' when we do NOT have a right to assume the fact; we usually aim for contradiction or do case analysis here.
Apply. It is a misconception that mathematicians do not apply what we have. We often apply theorems, maps, and transforms to suitable objects in order to get what we need.

Disclaimer:

The lyrics belong to the Klein Four Group.
As I have not yet taken topology when I wrote this, I cannot guarantee the correct links for topology terminology; maybe I'll update them some day.
Some terms just do not have a proper Mathworld page, I try to link them to similar pages, these include, say, `smooth.'
I try to narrow down some terms that have multiple meanings when there does not exist a general definition page:
e.g. `kernel.' There is no definition of kernel by itself, so I used module kernel as that relates more closely to a rank-one map.
Some are not mathematical definitions but things mathematicians say: `Q.E.D.' had a page of its own, the other ones I had to write myself. I cannot guarantee the correctness of these.
If you think some links can be altered to more correctly convey the meaning wanted, feel free to let me know.
If you think I am dumb, you could also contact me.
If you have more of these wonderful songs, share them with me.
If you failed a test because of this song, I am not sorry.
If you failed a test because of this webpage, feel free to complain.
My level of living has been richly elevated by the existence of this song, yay.
I am writing random gibberish here.
Actually the use of these random gibberish is to push the definitions upward.
Or else you might think I do not know how to code anchors.
Now if you are reading this, you are wasting time.
If you are still reading this, I am wasting your time.
``10^19 neutrinos will speed harmlessly through your brain and body in the time it takes to read this sentence. By the time you have read this sentence, they will be farther away than the moon.''
That was a quote I got from my relativity textbook.
Now by reading this sentence, the outcome of your life has been irrevocably altered.
What was going to happen if you had not read this is lost for ever.
Now I got this notion from Ling Yang.
No I am not blood-related (as for as we know of) to Ling.
If this much gibberish still did not make the page long enough, then there are two possibilities:
- You are using very small font: Use bigger font, it will be better for your eyes.
- You are using a very big visual display device (monitor, screen, printer, whatever): You are too rich, help poor children in Uganda!
If you get the reference, you are amazing and I like you, long live VIM.
If you have not guessed, vi is the program I use to do all my coding and all my daily text file editing needs.

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