Monthly Archives: September 2011

The decadic metric

Posted on September 28, 2011 by Brent

Continuing my series of posts exploring the decadic numbers… in my previous post, I explained that we will define a new “size function”, or metric, different from the usual “absolute value”, and written . Two numbers will be “close to” … Continue reading →

Posted in arithmetic, number theory, pattern | Tagged , , , , , , , | 5 Comments

What does “close to” mean?

Posted on September 22, 2011 by Brent

Continuing from last time, consider the (normal, decimal) number with an infinite number of 3’s after the decimal point. Now, you probably know that this represents . But why? How do we define what such an infinite sequence of digits … Continue reading →

Posted in convergence, number theory | Tagged , , , , | 3 Comments

An invitation to a funny number system

Posted on September 17, 2011 by Brent

Consider the equation Solving this equation is no sweat, right? Let’s do it. First, we subtract from both sides: Now we can factor an out of the left side: Now, if the product of two things is zero, one of … Continue reading →

Posted in arithmetic, number theory | Tagged , , , | 8 Comments

A curiosity

Posted on September 14, 2011 by Brent

From Futility Closet, a fun blog of random tidbits I enjoy reading, comes the following curious sequence of equations, attributed to J.A.H. Hunter: I managed to extend this pattern for a few more digits before I got bored. Does it … Continue reading →

Posted in arithmetic, modular arithmetic, number theory, pattern | 20 Comments

Some words about Post without words #2

Posted on September 11, 2011 by Brent

My previous post displayed this picture: As Yuriy Kashnikov guessed, I made this picture using diagrams, a Haskell library I am developing for creating images like this. (You can see the source code for this picture here.) If you haven’t … Continue reading →

Posted in counting, pascal's triangle, pattern, pictures | Tagged , , , , | 4 Comments

Post without words #2

Posted on September 6, 2011 by Brent
Posted in counting, pascal's triangle, pattern, pictures, posts without words | 10 Comments