### Meta

### Categories

- algebra (47)
- arithmetic (86)
- books (35)
- calculus (7)
- challenges (59)
- combinatorics (31)
- complex numbers (6)
- computation (83)
- convergence (9)
- counting (38)
- famous numbers (49)
- fibonacci (18)
- fractals (13)
- games (34)
- geometry (73)
- golden ratio (8)
- group theory (28)
- humor (8)
- induction (8)
- infinity (19)
- iteration (24)
- links (77)
- logic (12)
- meta (43)
- modular arithmetic (30)
- number theory (108)
- open problems (11)
- paradox (1)
- pascal's triangle (8)
- pattern (106)
- people (23)
- pictures (74)
- posts without words (44)
- primes (57)
- probability (9)
- programming (20)
- proof (93)
- puzzles (18)
- recursion (16)
- review (25)
- sequences (28)
- solutions (31)
- teaching (16)
- trig (3)
- Uncategorized (6)
- video (19)

### Archives

- August 2021 (2)
- June 2021 (3)
- May 2021 (1)
- March 2020 (4)
- February 2020 (1)
- January 2020 (7)
- December 2019 (4)
- November 2019 (2)
- October 2019 (5)
- September 2019 (7)
- August 2019 (3)
- July 2019 (5)
- May 2019 (4)
- April 2019 (2)
- March 2019 (3)
- February 2019 (3)
- January 2019 (4)
- November 2018 (3)
- October 2018 (4)
- September 2018 (4)
- August 2018 (6)
- July 2018 (2)
- June 2018 (5)
- May 2018 (3)
- April 2018 (5)
- March 2018 (4)
- February 2018 (3)
- January 2018 (4)
- December 2017 (3)
- November 2017 (3)
- October 2017 (1)
- September 2017 (1)
- July 2017 (4)
- June 2017 (4)
- May 2017 (9)
- April 2017 (7)
- March 2017 (5)
- February 2017 (4)
- January 2017 (3)
- December 2016 (4)
- November 2016 (6)
- October 2016 (6)
- September 2016 (2)
- August 2016 (5)
- July 2016 (2)
- June 2016 (4)
- May 2016 (4)
- April 2016 (2)
- March 2016 (3)
- February 2016 (9)
- January 2016 (8)
- December 2015 (5)
- November 2015 (29)
- August 2015 (3)
- June 2015 (2)
- April 2015 (1)
- May 2014 (1)
- December 2013 (1)
- October 2013 (1)
- July 2013 (1)
- June 2013 (1)
- May 2013 (1)
- April 2013 (3)
- March 2013 (3)
- February 2013 (2)
- January 2013 (5)
- December 2012 (3)
- November 2012 (4)
- October 2012 (5)
- September 2012 (1)
- August 2012 (4)
- July 2012 (1)
- June 2012 (6)
- May 2012 (2)
- April 2012 (3)
- March 2012 (1)
- February 2012 (4)
- January 2012 (5)
- December 2011 (1)
- November 2011 (7)
- October 2011 (4)
- September 2011 (6)
- July 2011 (2)
- June 2011 (4)
- May 2011 (5)
- April 2011 (2)
- March 2011 (4)
- February 2011 (1)
- January 2011 (1)
- December 2010 (1)
- November 2010 (4)
- October 2010 (2)
- September 2010 (1)
- August 2010 (1)
- July 2010 (1)
- June 2010 (2)
- May 2010 (3)
- April 2010 (1)
- February 2010 (6)
- January 2010 (3)
- December 2009 (8)
- November 2009 (7)
- October 2009 (3)
- September 2009 (3)
- August 2009 (1)
- June 2009 (4)
- May 2009 (5)
- April 2009 (4)
- March 2009 (2)
- February 2009 (1)
- January 2009 (7)
- December 2008 (1)
- October 2008 (2)
- September 2008 (7)
- August 2008 (1)
- July 2008 (1)
- June 2008 (1)
- April 2008 (5)
- February 2008 (4)
- January 2008 (4)
- December 2007 (3)
- November 2007 (12)
- October 2007 (2)
- September 2007 (4)
- August 2007 (3)
- July 2007 (1)
- June 2007 (3)
- May 2007 (1)
- April 2007 (4)
- March 2007 (3)
- February 2007 (7)
- January 2007 (1)
- December 2006 (2)
- October 2006 (2)
- September 2006 (6)
- July 2006 (4)
- June 2006 (2)
- May 2006 (6)
- April 2006 (3)
- March 2006 (6)

# Tag Archives: decadic

## Computing with decadic numbers

[This is the ninth, and, I think, final 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 … Continue reading

## u-tube

[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 decadic, Haskell, idempotent, streaming, u
2 Comments

## A self-square number

[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 decadic, idempotent, self, square
12 Comments

## More fun with infinite decadic numbers

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 decadic, decimal, fractions, integers, representation
4 Comments

## Infinite decadic numbers

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 decadic, negative, numbers
7 Comments

## 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