http://io9.com/5977095/why-we-should-sw ... ing-system
I've thought about repeating decimals, and irrational numbers before, never with anything like real mathematical rigor, but it did occur to me that maybe the issue with them has to do with our use of a particular number system.
If 1/3 is not a number we can really represent with base ten, doesn't that say something is wrong with base ten?
I'm not convinced we should all drop base ten and start using base 12, but the above is an interesting article discussing the possibilities of a different number system, and it might give people who don't normally think about these things a little something to chew on.
-
In total there are 9 users online :: 0 registered, 0 hidden and 9 guests (based on users active over the past 60 minutes)
Most users ever online was 1086 on Mon Jul 01, 2024 9:03 am
What do ya got there... Numbers?
Forum rules
Do not promote books in this forum. Instead, promote your books in either Authors: Tell us about your FICTION book! or Authors: Tell us about your NON-FICTION book!.
All other Community Rules apply in this and all other forums.
Do not promote books in this forum. Instead, promote your books in either Authors: Tell us about your FICTION book! or Authors: Tell us about your NON-FICTION book!.
All other Community Rules apply in this and all other forums.
- johnson1010
-
Tenured Professor
- Posts: 3564
- Joined: Mon Mar 23, 2009 9:35 pm
- 15
- Location: Michigan
- Has thanked: 1280 times
- Been thanked: 1128 times
What do ya got there... Numbers?
In the absence of God, I found Man.
-Guillermo Del Torro
Are you pushing your own short comings on us and safely hating them from a distance?
Is this the virtue of faith? To never change your mind: especially when you should?
Young Earth Creationists take offense at the idea that we have a common heritage with other animals. Why is being the descendant of a mud golem any better?
-Guillermo Del Torro
Are you pushing your own short comings on us and safely hating them from a distance?
Is this the virtue of faith? To never change your mind: especially when you should?
Young Earth Creationists take offense at the idea that we have a common heritage with other animals. Why is being the descendant of a mud golem any better?
- Dexter
-
- I dumpster dive for books!
- Posts: 1787
- Joined: Sun Oct 24, 2010 3:14 pm
- 13
- Has thanked: 144 times
- Been thanked: 712 times
Re: What do ya got there... Numbers?
Interesting, never thought about that before.
I always thought the metric system of measurements made a lot more sense, but would be nearly impossible for the US to switch to. This would probably be even harder to do.
I always thought the metric system of measurements made a lot more sense, but would be nearly impossible for the US to switch to. This would probably be even harder to do.
-
-
Master Debater
- Posts: 23
- Joined: Sun Oct 07, 2012 9:38 pm
- 11
- Has thanked: 8 times
- Been thanked: 16 times
- Contact:
Re: What do ya got there... Numbers?
There are some pretty salient features here about why using a base-12 number system would be more efficient, but as noted, the change would be horrendous to navigate. Most of us that were raised on base-10 would spend our lives thinking in base-10 and have to do a lot of conversions all the time.
The fraction thing gets a crappy treatment here. In reality, we run into repeating decimals with rational numbers in every case where the denominator of the fraction has in it a prime not included in the prime factorization of the base. So, in base 10, if the denominator of the fraction only contains powers of 2 and 5 in its prime factorization, the decimal terminates. If it contains any other prime, the decimal expansion repeats.
If we changed to base-12, fractions like 1/2, 1/3, and 1/4 would be "nice," but fractions like 1/5, 1/7, 1/11, 1/35, 1/10, 1/15, 1/4, etc. would still have repeating decimal expansions. The only way to get around repeating decimal expansions is to have "base-infinity" notation (which functionally would mean that every number gets its own symbol, which would be useless).
Interesting piece, though, I guess. I don't see it as being imminently practical given the enormous investment that would be involved in changing over.
The fraction thing gets a crappy treatment here. In reality, we run into repeating decimals with rational numbers in every case where the denominator of the fraction has in it a prime not included in the prime factorization of the base. So, in base 10, if the denominator of the fraction only contains powers of 2 and 5 in its prime factorization, the decimal terminates. If it contains any other prime, the decimal expansion repeats.
If we changed to base-12, fractions like 1/2, 1/3, and 1/4 would be "nice," but fractions like 1/5, 1/7, 1/11, 1/35, 1/10, 1/15, 1/4, etc. would still have repeating decimal expansions. The only way to get around repeating decimal expansions is to have "base-infinity" notation (which functionally would mean that every number gets its own symbol, which would be useless).
Interesting piece, though, I guess. I don't see it as being imminently practical given the enormous investment that would be involved in changing over.
Writer, mathematician, Southerner, atheist.
Author of God Doesn't; We Do: Only Humans Can Solve Human Challenges
Or see my blog: God Doesn't; We Do--Blog
God doesn't exist, almost surely.
Author of God Doesn't; We Do: Only Humans Can Solve Human Challenges
Or see my blog: God Doesn't; We Do--Blog
God doesn't exist, almost surely.