User:Gordon Stangler

Hello. I am an unemployed white male whom is interested in physics and mathematics. I have edited and created a lot of pages here on Wikipedia, but the vast majority of said creations is as an anon user, since I am in general too lazy to sign in.

My pride and joy is the page on Perfect Squares. ^_^

The list of unsolved problems is also useful.

I guess I consider myself a WikiGnome/WikiFaerie. All is good.

I hold research interests in Black Hole Thermodynamics, Quantum Field Theories, Four dimensional wakes and waves, Cosmological/ Big Bang theories, Prime numbers, the Navier-Stokes equations, Dirichlet L functions, Dirichlet characters with generalized Zeta functions, the Birch and Swinnerton-Dyer Conjecture, and faster then light travel. Limits, epsilon-delta proofs, and Goldbach's conjecture are the bane of my existence.

Very Quick Introduction to Sets

A set is a collection of mathematical objects, often referred to as elements. For example,

A = {2,3,5,7,11)

is a set, as is

B = (blue, purple, green).

Examples of Sets

$\mathbb {P}$, the set of all prime numbers, $\mathbb {N}$, the set of all natural numbers, $\mathbb {Z}$, the set of all integers, $\mathbb {R}$, the set of all real numbers, and $\mathbb {C}$, denoting the set of all complex numbers. We also have the empty set, which has no elements in it; and the null set, which contains only the null element ø.

Membership

To say an element 'm' is in 'M', we use $\in .$

$4\in \mathbb {N}$, and $4\notin \mathbb {P}$

Other

$\forall$ The upside down A is read 'for all'.

$\exists$ The backwards E is read 'there exists'.

$\forall x\in \mathbb {N} <100$, x has two or fewer digits.

$\exists x\forall y[x<y]$ means there is some element x, less then all the elements y in our set. This is of course the definition of lower bound.

Boolian Logic

T = true, F = false

$\land$ = AND (logical conjunction)

$\lor$ = OR (logical disjunction)

$\rightarrow$ = IF-THEN

$\iff$ IFF (IF AND ONLY IF), equivalent to XNOR (exclusive nor).

$P$	$Q$	$P\land Q$	$P\lor Q$	$P\iff Q$	$P\rightarrow Q$
F	F	F	F	T	T
F	T	F	T	F	T
T	F	F	T	F	F
T	T	T	T	T	T