They should have sent a poet

Finite Simple Group (of Order Two)

Oh god. Commence the groaning. It’s a Valentines-themed song using math lingo. It’s probably one of the nerdiest things I’ve ever seen. I seem like an uneducated barbarian (pre-fire era) before these guys. But it’s amusing. It’s kinda fun trying to identify which words are math keywords.  Once you start wiki-ing them, it kinda makes you  marvel how much knowledge mankind has acquired, and how it could all be lost so quickly given the right (or wrong) catastrophe.

Most of the terms are beyond the math I learned in college, but one of the commenters (Nightbreeze1) attempted to explain them:

Kernel: All of the domain of a function (map) which is mapped to zero

Rank-one: meaning the range-space has dimension one (such as the real line!)

See zeroes: he’s in the kernel!

Smooth path: A smooth function has derivatives of all orders, a path is a special type of function (in some sense)

Continuous: meaning without ‘holes’ or ‘jumps’, as in a function

Upper bound: Just an upper bound on some quantity, used often

Axiom of Choice: Controversial, but famous, axiom. gogo wiki

Relation, well-defined, function, proposition: All terms you encounter every other paragraph of any math book

Finite simple group of order two: Ironically, ‘simple’ is too complicated to explain here. A group is a mathematical object measuring symmetry (wiki!) and the ‘order’ is just the number of elements in it :)

Identity: Identity element or ~map in a group is that which leaves everything unchanged

Tensor: Rather complicated mathematical object.. (wiki)

Without loss of generality: WLOG, found in manymanymany mathproofs, which makes it funny

‘Quotient out’: Operation done on groups/spaces/etc, very important!

Map-image : Map is a function, the image is the image :)

one-to-one : Property of a function, meaning for every element in the image of a function, precisely 1 is mapped into it from the domain

Equivalence: Equivalence relation, found often… wiki

Bundle: very complicated, wiki won’t help much

wedge between two-forms: Too complicated

Complexified: Extending ‘something’ to incorporate the complex numbers (not just reals)

Simply connected: Property of a set, meaning every two points can be connected via a path (think circle!)

Open-dense: Properties of sets…

System: System of sets :D collection of sets

Finite limit: Well, this combined with the previous line has something to do with a very abstract limiting process, probably in terms of a set of systems. This could be in the context of sigma-algebra’s or just general topology or any other context in which limits ‘in some sense’ may arise..

Operator, class : Both words found often. Operator is a special kind of function, class is just a class (we class our operators!)

Mirror pair: Forget it

Forgetful functors: nah.. can’t explain this either

Associative : Algebraic property! (a+b)+c = a+(b+c) meaning order of operation is irrelevant (all groups have this)

Free: Another groupproperty..definition a bit too complicated

corollary: Something found in every math textbook after many of the theorems and lemma’s

Q.E.D.: Everybody knows this one, Quod Erat Demonstrandum!

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One Response to “Finite Simple Group (of Order Two)”

  1. mathematician says:

    Simply connected actually means that any two paths with the same endpoint can be connected by a ‘path of paths’, so ironically the circle you use as an example is actually NOT simply connected.

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