Category Archives: infinity

u-tube

Posted on January 10, 2012 by

[This is the eighth in a series of posts on the decadic numbers (previous posts: A curiosity, An invitation to a funny number system, What does "close to" mean?, The decadic metric, Infinite decadic numbers, More fun with infinite decadic … Continue reading →

Posted in computation, convergence, infinity, iteration, modular arithmetic, number theory, programming | Tagged , , , , | 2 Comments

A self-square number

Posted on January 4, 2012 by

[This is the seventh in a series of posts on the decadic numbers (previous posts: A curiosity, An invitation to a funny number system, What does "close to" mean?, The decadic metric, Infinite decadic numbers, More fun with infinite decadic … Continue reading →

Posted in arithmetic, infinity, iteration, modular arithmetic, proof | Tagged , , , | 12 Comments

More fun with infinite decadic numbers

Posted on October 28, 2011 by

This is the sixth in a series of posts on the decadic numbers (previous posts: A curiosity, An invitation to a funny number system, What does “close to” mean?, The decadic metric, Infinite decadic numbers). Last time I left you … Continue reading →

Posted in arithmetic, infinity, number theory | Tagged , , , , | 4 Comments

Infinite decadic numbers

Posted on October 19, 2011 by

To recap: we’ve now defined the decadic metric on integers by where is not divisible by 10, and also . According to this metric, two numbers are close when their difference is decadically small. So, for example, and are at … Continue reading →

Posted in arithmetic, convergence, infinity, number theory | Tagged , , | 7 Comments

Book review: Roads to Infinity

Posted on July 5, 2011 by

What is infinity? What is proof? These are two of the biggest questions mathematicians have grappled with over the years. In this well-written and fascinating book, John Stillwell takes us on a tour through some of the answers to these … Continue reading →

Posted in arithmetic, books, computation, induction, infinity, logic, proof, review | Tagged , , ,

Rational numbers and decimal expansions

Posted on September 7, 2008 by

As you may remember from school, rational numbers have a terminating or eventually repeating (periodic) decimal expansion, whereas irrational numbers don’t. So, for example, 0.123123123123…, with 123 repeating forever, is rational (in fact, it is equal to 41/333), whereas something … Continue reading →

Posted in infinity, iteration, number theory, pattern | Tagged , , | 9 Comments

Recounting the Rationals, part II (fractions grow on trees!)

Posted on January 7, 2008 by

Today I’d like to continue my exposition of the paper “Recounting the Rationals”, which I introduced in a previous post. Recall that our goal is to come up with a “nice” list of the positive rational numbers — where by … Continue reading →

Posted in infinity, number theory, pattern, recursion, sequences | 22 Comments

Carnival of Mathematics #23: Haiku Edition

Posted on December 28, 2007 by

Welcome to the 23rd Carnival of Mathematics: Haiku Edition! First, I must apologize for the delay: I usually have very little trouble with my hosting provider, but of course it went down just when the CoM was supposed to be … Continue reading →

Posted in algebra, books, calculus, challenges, counting, fractals, geometry, infinity, links, meta, number theory, pascal's triangle, pattern, people, sequences, trig, video | 17 Comments

Recounting the Rationals, part I

Posted on December 27, 2007 by

This is the first in a series of posts I’m planning to write on the paper “Recounting the Rationals“, by Neil Calkin and Herbert Wilf, mathematicians at Clemson University and the University of Pennsylvania, respectively. I’m really excited about it, … Continue reading →

Posted in counting, infinity, number theory, pattern, sequences | 19 Comments

Open problems: Twin prime conjecture

Posted on April 10, 2007 by

Oops, so much for posting once a week! My excuse is that I’ve been hard at work on my book. Well, nothing to do but get right back at it. I promise* I will be better** about posting regularly*** from … Continue reading →

Posted in challenges, famous numbers, infinity, primes | 3 Comments