What's a good numerical base?

[Cort Haus]

Originally posted by Asher
Base 16 is the only reasonable base.

Mein Gott! Image the music we could play with eight fingers on each hand. And the instruments we would devise. It would give a new meaning to power-chords.

[Alinestra Covelia]

Originally posted by Alinestra Covelia

Yes, but is that "12 bucks" in base 16, 12, or 6?

The answers I was looking for were:

Base-16: 18 in base-10.
Base-12: 14 in base-10.
Base-6: 8 in base-10.

I'm not entirely sure why it took me this long to do this myself. Normally I'm not this obtuse, I swear!

[KrazyHorse]

Base (pi)^e

Nice to have a base whose transcendentality is unknown

[Krill]

That would be so cool

[Thue]

I support that. Integer bases are overrated .

Edit: once I figure out how to write numbers in it - it doesn't seem to be possible, since the whole base idea depends on the base being an integer .

[Alinestra Covelia]

^

Thue, that's one of the best posts I've seen in a while!

[Q Classic]

Originally posted by Alinestra Covelia


The answers I was looking for were:

Base-16: 18 in base-10.
Base-12: 14 in base-10.
Base-6: 8 in base-10.

I'm not entirely sure why it took me this long to do this myself. Normally I'm not this obtuse, I swear!

Okay, I'm not sure why my maths were so wonky, or how I just parsed that comment wrong.

Must've been the time I spent as a Mrs. Because math's HARD! And so's Engrish!

[Boris Godunov]

I'm going to go with Tom Lehrer on this one, and suggest Base 8.

[KrazyHorse]

Originally posted by Thue
I support that. Integer bases are overrated .

Edit: once I figure out how to write numbers in it - it doesn't seem to be possible, since the whole base idea depends on the base being an integer .

http://www.springerlink.com/content/w2g3k1m3ph455022/

[KrazyHorse]

That's why it would be interesting to have the transcendentality/algebraic quality of the base unknown.

[Thue]

After posting that comment I was actually considering that some real numbers could represent all numbers, but was too lazy to work out the math .

Or can every real number base represent all numbers? It doesn't seem impossible to work out, but if I wanted to do math right now I would not be posting to Apolyton . Edit: no, of course they can't.

Of course a big point of a number system is being able to express all numbers on the real line. As I said above, there are non-integer bases which can not express all numbers. Is there a non-integer base which can express all numbers? Probably not.

[Thue]

(I actually read the preview page you linked to)

[Thue]

Just for the record, I just proved that no non-integer base can represent all numbers on the continuous number line.

[Cort Haus]

Maths geeks

[KrazyHorse]

Originally posted by Thue
After posting that comment I was actually considering that some real numbers could represent all numbers, but was too lazy to work out the math .

Actually, this is a serious area of inquiry. Unless you are a research quality mathematician, it is probably going to be impossible for you to do this.

I've basically got an undergraduate degree in math and I'm not qualified to really go into depth on this.