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# Monthly Archives: September 2011

## The decadic metric

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 decadic, distance, integers, metric, number line, numbers, p-adic, soup
5 Comments

## What does “close to” mean?

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 absolute value, Cauchy, distance, limit, sequence
3 Comments

## An invitation to a funny number system

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

## A curiosity

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

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 binomial coefficients, diagram, Hasse, Pascal, subset
4 Comments