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# Category Archives: infinity

## Rational numbers and decimal expansions

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

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

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

## Recounting the Rationals, part I

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

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

## New bookshelf entry: The Book of Numbers

After seeing John H. Conway and Richard Guy‘s The Book of Numbers cited in yet another interesting article/book/whatever, I finally decided that I clearly had to read it. (It seems to get cited a lot in certain circles.) I wasn’t … Continue reading

Posted in books, famous numbers, geometry, golden ratio, infinity, links, primes
3 Comments

## The Mandelbrot Set

For those of you already familiar with the Mandelbrot Set, I suppose this will be like visiting with an old friend. For those of you who aren’t — you’re in for a treat! Okay, you say, that looks pretty cool … Continue reading

Posted in convergence, fractals, infinity, iteration
1 Comment