Formal Proof of the Infinitude of Primes

In the Infinitude of Primes post, we have shown intuitively that there are infinitely many primes. In this post, we use our intuitive proof to create a more formal proof. The proof was supposedly constructed by Euclid and was shown in his book, The Elements.

Euclid (via Wikimedia)

We are going to use the proof strategy called proof by contradiction. Our proof is summarized as follows: » Read more

Math and Multimedia Carnival Criteria for Selection of Articles

The Mathematics and Multimedia Blog Carnival is now accepting articles  for the next issue. Although any math article might be accepted, below are the Revised Criteria for Blog Carnival Selection.  This will be characteristics of the articles that will be prioritized.  Articles with no links are done, but not yet posted.

1. Connection between and among different mathematical concepts

2. Connections between math and real life; use of real-life contexts to explain mathematical concepts

3. Clear and intuitive explanation of topics not discussed intextbooks, hard to understand, or  difficult to teach

4. Proofs of mathematical theorems in which the difficulty of the explanation is accessible to high school students

5. Intuitive explanation of higher math topics, in which the difficulty is accessible to high school students

6. Software introduction, review or tutorials

  1. Investigating Polyhedrons with Poly
  2. GeoGebra Tutorial Series

7. Integration of technology (Web 2.0, Teaching 2.0, Classroom 2.0), in teaching mathematics

  1. Using Google Sketchup in Teaching Mathematics
  2. Use of Google Docs  in Teaching Mathematics.

Mathematics and Multimedia Blog Carnival is still in its infancy, so please help spread the word about it. I would appreciate if bloggers who has benefitted from Mathematics and Multimedia, especially those whose article was accepted in the previous carnival, would announce it in their blogs.

To submit article the Math and Multimedia Blog Carnival, click  here.

The Math Teachers at Play Carnival and Carnival of Mathematics are also accepting math articles for their carnivals. Please do not duplicate submissions.

Erlina Ronda of Keeping Mathematics Simple will host the Mathematics and Multimedia blog carnival special edition on December 2010.  Her topic will be on Teaching Algebra Concepts. You can email her to submit in advance.

Photos: Wikipedia Concept Map by juhansonin, Mandelbrot Julia Section by Arenamontanus

Prime Series 2: The Intuition Behind The Infinitude of Prime Numbers

Note: This is the third part of the Prime Number Series

  1. Part I: Introduction to Prime Numbers
  2. Part III: Formal Proof of the Infinitude of Prime Numbers

In Introduction to Prime Numbers, we conjectured that the number of prime numbers is decreasing as the counting numbers increase. In this post, we discuss intuitively that there is no greatest prime, or that there are infinitely many prime numbers.

Before proceeding with our discussion, it is noteworthy to remember that a number can either be prime or composite. We also know that composite numbers are product of primes.

Fragment of the original "Elements" by Euclid (via Wikimedia).

» Read more

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