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Prime Numbers - Proofs

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When seeing isn't believing. Platonic Realms Interactive Mathematics Encyclopedia. The primes keep going up. There is an infinite number of primes. Here's one proof. The primes keep going up. Multiplying the primes and adding 1. Multiplying the primes and adding 1. In this proof by contradiction one assumes there's a limited number of primes, but it turns out you can create a new prime number larger than those in your original list. We have a contradiction, so our original assumption was false. In the se...

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Jape - Proofs

http://proofs.wikidot.com/jape

When seeing isn't believing. Platonic Realms Interactive Mathematics Encyclopedia. UPDATE 11 March 2009. Jape now works on Tiger (Apple's Mac OS X 10.4). Dr. Bornat sent me a new version compiled by his collaborator, Bernard Sufrin, and it worked fine. I assume jape.org.uk. Will soon add this version for download. I became interested in Jape ( jape.org.uk. While reading Richard Bornat. Proof and Disproof in Formal Logic: An introduction for programmers. How to Use Jape. And his 2005 book,. From a more fr...

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Fundamental Theorem Of Arithmetic - Proofs

http://proofs.wikidot.com/fundamental-theorem-of-arithmetic

When seeing isn't believing. Platonic Realms Interactive Mathematics Encyclopedia. Fundamental Theorem Of Arithmetic. The proof by contradiction and proof by induction are very similar. Any integer greater than 1 can be factored into primes in one and only one way. We can show this factoring happens in. One way, and we then show it happens in. Any integer greater than 1 can be factored into primes. Be factored into primes then we get a contradiction. Be factored into primes then we get a contradiction.

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Add A Page - Proofs

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When seeing isn't believing. Platonic Realms Interactive Mathematics Encyclopedia. Page revision: 0, last edited: 23 Feb 2009 20:02. Powered by Wikidot.com. Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. A Wiki for Hammerfall RPG on Facebook and Myspace. The best text-based mature RPG database that anyone can edit! A Shining Brainless Beacon. I Have a Special Plan for This World. Obsidian Conflict Map Database.

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Templates - Proofs

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When seeing isn't believing. Platonic Realms Interactive Mathematics Encyclopedia. This is a basic article template, excerpted from the (at the time of this writing) current version of the article, Fundamental Theorem of Algebra. Here is the source:. Remove initial space that was inserted so include code would show up- ]. And here is how it's rendered:. 8220;A polynomial of positive degree over the field $ mathbb{C}$. Of complex numbers has a root in $ mathbb{C}$. The polynomial $x 2 1$. Begin{align} bar...

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Fundamental Theorem Of Algebra - Proofs

http://proofs.wikidot.com/fundamental-theorem-of-algebra

When seeing isn't believing. Platonic Realms Interactive Mathematics Encyclopedia. Fundamental Theorem Of Algebra. This reworked proof draws from the explanation in [ 3. Of Gauss's initial 1797 proof and some background details. The initial sketch in that source does not detail how the two curves are constrained to provide a common solution. Any complex polynomial must have a complex root. Note that $a i, z in mathbb{C}$. Any complex function $P(z) = a n z n a {n-1} z {n-1} cdots a 0$. P(z 0) = 0$. Pleas...

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Square Root Of 2 - Proofs

http://proofs.wikidot.com/square-root-of-2

When seeing isn't believing. Platonic Realms Interactive Mathematics Encyclopedia. Square Root Of 2. There are many proofs that the square root of 2 is irrational. Here are two related ones. Assume ratio has no common factors. Don't assume ratio has no common factors. This version simply finesses the lowest common denominator presentation. The square root of 2 is irrational. Because the square root of 2 is not rational. Because assuming the square root of 2 is rational produces a contradiction. Divide bo...

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Linearly Independent Automorphisms - Proofs

http://proofs.wikidot.com/linearly-independent-automorphisms

When seeing isn't believing. Platonic Realms Interactive Mathematics Encyclopedia. From Galois theory. I've rewritten the presentation in [ 1. 124, p. 106]. Definition of “Linearly Dependent” and “Linearly Independent”. 8220;If $ phi 1, phi 2, ldots, phi n$. Are distinct automorphisms of $E$. Then the set $ { phi 1, phi 2, ldots, phi n }$. Is linearly independent over $E$. Definition of “Linearly Dependent” and “Linearly Independent”. From the start of the previously cited 124 of [ 1. Then the set $ { ph...

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A Hyperwelcome - Proofs

http://proofs.wikidot.com/start

When seeing isn't believing. Platonic Realms Interactive Mathematics Encyclopedia. This is a (. Limited) wiki on proofs. I've always been interested in proofs, since they seem both precise and vague, obvious and enigmatic at the same time. I started out rewriting proofs I've read, including proofs of why the square root of 2 is irrational. And why the number of primes is infinite. Another proof looks at the Fundamental Theorem of Arithmetic. And the demand rings out: “Why? 8221; The chain of. A copy of t...

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Subscript Problem - Proofs

http://proofs.wikidot.com/sandbox-subscript-problem

When seeing isn't believing. Platonic Realms Interactive Mathematics Encyclopedia. An apparent bug with Wikidot.com syntax makes a subscript of just 0 invisible. This code:. The workaround I discovered was to specify the 0 as raw unparsed text. So:. Invisible 0:* / x/ , 0, (regular syntax) * Visible 0:* / x/ , @ 0@ , (making 0 unparsed). You may have noticed I wrote (zero) not 0 in the first column of the table. While making the table I found that. 171; (you're presumably. Seeing a bold zero). See pages ...