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# User:Ircher

## About Me

I have been active on the site since November 2015.

### Contact Me

If you would like to leave me a message on the wiki, please post it at User Talk:Ircher. Be sure to add a signature. If you would like to contact me via the forums, please shoot me a PM.

Unless it is marathon weekend and related to a marathon, **please do not try to contact me by Discord.** Contacting me on the forums by PM is almost always going to be the fastest way to contact me. In the case of Discord, I don't always receive notifications, and I don't frequently check Discord unless there is a reason for me to do so.

## Misc Stuff

### Other Games I Host

- Level Up 2: Dice-Rolling Fighting Game
**Ended**- A game hosted in The Whole Sort of General Mish Mash where you fight monsters in order to gain experience. The game starts out as a very simple dice-rolling game with very few options, but as you level up and progress, you gain access to new skills, spells, and abilities that can change the way battles operate. To join, just post /in in the thread. - Nomic: The Constitution Game
**Ended**- A game hosted in The Whole Sort of General Mish Mash where you through the cooperation of others shape the rules of the game. - Nomic: Wiki Edition
**Ended**- A game hosted in The Whole Sort of General Mish Mash where you through the cooperation of others shape the rules of the game. This version has its official status recorded on this wiki page. - Investment$ IX
**Ended**- A game hosted in The Whole Sort of General Mish Mash where you play the role of a trader on the stock market with the goal of making as much money as you can.

### Links

Player Ratings (Based on games I've played as well as games I've modded.)

Code Templates for Modding Games

### Theorem of the Week Archive

- 03/24/2022 to 05/31/2022:
**Unique Factorization in Z[x]**: Every nonzero non-unit polynomial in Z[X] (the ring of polynomials with integer coefficients) can be written as a product of irreducible polynomials (coming from Z[x]). Moreover, the factorization is unique up to the order and signs of the factors. - 02/12/2022 to 03/24/2022: The
**Pigeonhole Principle**: If you have more pigeons than holes, then there is at least one hole that contains multiple pigeons. - 01/01/2022 to 02/12/2022: The
**Three Reflections Theorem**: In the Euclidean plane, any distance-preserving map (also called an isometry) is the product (i.e.: composition) of at most three reflections. - 12/17/2021 to 01/01/2022: The
**Socks-Shoes Property**: To invert the action of putting your socks on first and then your shoes, you must first take off your shoes and then take off your socks. In symbols: for group elements a and b, (ab)^{-1}= b^{-1}a^{-1}. - 12/11/2021 to 12/17/2021: The
**Fundamental Theorem of Finite Abelian Groups**: Every finite Abelian group is isomorphic to a direct product of cyclic groups of prime-power order. - 11/17/2021 to 12/11/2021:
**Gödel’s First Incompleteness Theorem**: If F is a formal system capable of performing a certain amount of arithmetic and F is consistent, then we cannot prove every true statement in F. - 11/08/2021 to 11/17/2021: The
**Pasting Lemma**: If f : A -> Y and g : B -> Y are continuous and A, B are open (closed) and agree on A ∩ B, then you can combine them to form a single continuous function h : A ∪ B -> Y where h(x) = f(x) on A and h(x) = g(x) on B. - 11/03/2021 to 11/08/2021:
**Fermat's Little Theorem**: If a is an integer and p is a prime, then p divides (a^{p}- a). - 10/28/2021 to 11/03/2021:
**Lagrange's Theorem**(Group Theory): If G is a finite group, and H is a subgroup of G, then the order of H divides the order of G. Furthermore, the number of distinct left (right) cosets of H in G is given by the order of G divided by the order of H. - 10/21/2021 to 10/28/2021: The
**Incredible Shrinking Theorem**: A topological space X is normal if and only if for every pair of open sets U and V that union to X, there exist open sets U' and V' such that U' ∪ V' = X, the closure of U' is a subset of U, and the closure of V' is a subset of V. - 09/16/2021 to 10/21/2021: The
**Heine-Borel Theorem**: This theorem characterizes compactness (the next best thing to being finite) on the real line: a set is compact if and only if 1) it is closed and bounded 2) every sequence in the set has a convergent subsequence or 3) every open cover has a finite subcover. - 09/07/2021 to 09/16/2021: The
**Schroeder-Berstein Theorem**: If you have a one-to-one function from the set A to the set B and a one-to-one function from the set B to the set A, then the sets A and B are the same cardinality. - 08/31/2021 to 09/07/2021: The
**Squeeze Theorem**: If a function h is "squeezed" between two other functions f and g and the limit of f at x is equal to the limit of g at x, then the limit of h at x is the same value. - 08/23/2021 to 08/31/2021:
**Cantor's Power Set Theorem**: A set and its power set (the set of all subsets of that set) do not have the same cardinality (size). - 07/13/2021 to 08/23/2021:
**Fubini's Theorem**: The order of integration does not matter when integrating a continuous function on a rectangular region. This theorem generalizes to higher dimensions as well. - 06/16/2021 to 07/13/2021: The
**Undecidability of the Halting Problem**: It is impossible to create a Turing machine (read: "computer program") that can determine whether another Turing machine halts or not. - 06/07/2021 to 06/16/2021: The
**Parallel Postulate**: In Euclidean space, given a line L and a point P not on L, there exists exactly one line parallel to L that goes through P. - 05/18/2021 to 06/07/2021: The
**Central Limit Theorem**: The sum of a large number of independent and identically distributed random variables can be approximated well by a normal distribution. - 05/05/2021 to 05/18/2021: The
**Fundamental Theorem of Counting**: If there are m ways to do something and n ways of doing something else, then there are m * n ways of doing both actions. - 04/25/2021 to 05/05/2021: The
**Weierstrass Approximation Theorem**: Any continuous function can be approximated to any degree of accuracy by a polynomial function. - 04/16/2021 to 04/25/2021: The
**Fundamental Theorem of Calculus**, Part 2: The sum of all the "little changes" is equal to the net change on an interval. (In symbols, the definite integral from a to b of f'(x)dx is equal to f(b) - f(a).) - 04/10/2021 to 04/16/2021: The
**Fundamental Theorem of Calculus**, Part 1: Integration (finding the "total change") and differentiation (finding the "instantaneous rate of change") are inverse operations. - 04/01/2021 to 04/10/2021: The
**Four Color Theorem**: Any planar graph can be colored with at most four colors with no two regions sharing a common boundary having the same color. - 03/19/2021 to 04/01/2021: The
**Archimedean Property**: For any real number r, there exists a natural number n > r. - 03/11/2021 to 03/19/2021:
**Lagrange's Remainder Theorem**: Suppose f is differentiable N + 1 times and let S_n be the nth order Taylor polynomial of f. Then, there exists a |c| < |x| such that the error f(x) - S_{N}(x) equals^{f(N+1)(c) * xN+1}/_{(N + 1)!}. This theorem establishes a bound on the difference between a function and the Taylor polynomial being used to estimate it. - 02/27/2021 to 03/11/2021: The
**Cayley Tree Formula**: The number of distinct trees with n vertices (with the vertices labeled) is equal to n^{n-2}. - 02/19/2021 to 02/27/2021: The
**Differentiable Limit Theorem**: If a sequence of differentiable functions converge pointwise to a function f and the derivatives converge uniformly to a function g, then f' = g. In other words, under these conditions, we can interchange limits and derivatives. - 02/12/2021 to 02/19/2021: The
**Rank-Nullity Theorem**: For any matrix A with m rows and n columns, rank(A) + nullity(A) = n. An interpretation is that the number of bound variables plus the number of free variables equals the total number of variables. - 02/05/2021 to 02/12/2021: The
**Mean Value Theorem**: If a function is continuous on the interval [a, b] and differentiable on the interval (a, b), then there exists a point in (a, b) where the instantaneous rate of change equals the average rate of change. - 01/29/2021 to 02/05/2021: The
**First Theorem of Graph Theory**: The sum of the degrees of the vertices in a graph is equal to twice the number of edges. (The degree of a vertex is the number of edges incident with it.) - 01/21/2021 to 01/29/2021: The
**Intermediate Value Theorem**: Suppose a function f is continuous on a closed interval [a, b]. For any value L between f(a) and f(b), there exists a value c between a and b where f(c) = L. - 01/06/2021 to 01/21/2021:
**De Morgan's Laws**: The complement of A and B is not A or not B. The complement of A or B is not A and not B. - 01/01/2021 to 01/06/2021: The
**Quotient-Remainder Theorem**: For any natural number d and integer n, there exist unique integers q and r such that n = qd + r and 0 ≤ r < d. - 12/02/2020 to 01/01/2021: The
**Fundamental Theorem of Arithmetic**: Every positive integer greater than one can be expressed as a unique (up to order) product of primes. - 11/23/2020 to 12/02/2020: The
**Uncountability of the Reals**: There exist many more real numbers than natural numbers (i.e.: the reals have a greater cardinality than the natural numbers). - 11/17/2020 to 11/23/2020: The
**Invertible Matrix Theorem**: This theorem gives several conditions that are equivalent to a matrix having an inverse. - 11/09/2020 to 11/17/2020: The
**Axiom of Completeness**: Every nonempty subset of the real numbers that is bounded above has a least upper bound. - 11/02/2020 to 11/09/2020: The
**Alternating Series Test**: If a sequence (a_{n}) is a monotonically decreasing sequence that converges to zero, then the infinite alternating series Σ(-1)^{n}a_{n}converges. - 10/26/2020 to 11/02/2020: The
**Bolzano-Weierstrass Theorem**: Every bounded sequence of real numbers contains a convergent subsequence. - 10/15/2020 to 10/26/2020: The
**Projective Desargues Theorem**: If two triangles are in perspective from a point, then their pairs of corresponding sides meet on a line.

### Alternate Accounts

#### Hydras

- Heuristic_Arrow (Heuristically_Alone + Ircher)
- Maker_of_Zanos (BTD6_Maker + Ircher)
- Computer_Cat (RachMarie + Ircher)
- LAMIST (Creature + Ircher)
- Auscher (Ausuka + Ircher)
- The Searchers (SirCakez + Ircher)
- Mathematical Demon (Jake the Wolfie + Ircher)
- Sequence (Bell + Ircher)
- Emotion Calculus (Noraa + Ircher)
- War and Peace (samantha97 + Ircher)
- The Resistance (Titus + Ircher)

#### Alts

- 123456789
- The_Evil_Within
- Fundamental Theorem
- Covid 19
- In the beginning