what's 9 x 6?

Originally posted by smw6869
I have a small garden shed that's 9 x 6. I store my lawn mower in it.

GRANNY.

You were lucky - we lived in a cardboard box! 😕

Du....... 54; thats a no brainer. Pretty simple if U don't over analize it. Don't try to make a mole hill into a mountain. U asked a basic question :whats 9x6?" Not whats the base. Overanalization most likly will will make U question what should be oddvious... 🙄

Read the original post Einstein.

Originally posted by wolfgang59
Base 49

Yeah but what are the other symbols for the rest of the set? Base 16, 0-9 and A, B, C, D, E, F makes up that set so what is the symbol set for base 49? You run out of letters and numbers pretty soon🙂

Originally posted by sonhouse
Yeah but what are the other symbols for the rest of the set? Base 16, 0-9 and A, B, C, D, E, F makes up that set so what is the symbol set for base 49? You run out of letters and numbers pretty soon🙂

i know you were being cheeky, but i feel like this is an interesting point and would like to expound upon it!

you can make up whatever "symbols" you want, but the concept of the position system will remain the same - so rather than continuing the "letters and numbers" concept which eventually fails thanks to there being a finite number of "familiar" symbols, we go back to the position-based arabic numeral system and denote "places" by commas in a vector (usually.) just ask the egyptians and the romans what happens when you run out of symbols for representing sufficiently large or small numbers!

so though it may seem ill-conceived to need base 10 to even DENOTE base 49, it actually makes the concept much clearer and more useful.

(1,5) [also sometimes just written as 15] = 1*49^1 + 5*49^0.

and often for fractions in different bases (i.e. negative exponents in base 49), analogous to the decimal system, i've often seen a semicolon used in between the base^0 place and the base^-1 place. for example, the base 10 mixed number 49 and 54/2401ths would be written in base 49 as such:

(1,0;1,5) = 1*49^1 + 0*49^0 + 1*49^-1 + 5*49^-2

Originally posted by Aetherael
i know you were being cheeky, but i feel like this is an interesting point and would like to expound upon it!

you can make up whatever "symbols" you want, but the concept of the position system will remain the same - so rather than continuing the "letters and numbers" concept which eventually fails thanks to there being a finite number of "familiar" sym ...[text shortened]... ritten in base 49 as such:

[b](1,0;1,5) = 1*49^1 + 0*49^0 + 1*49^-1 + 5*49^-2[/b]

Have you ever heard of a book called "A number for your thoughts" by Malcom Lines?
It turns out he used to work at a start-up in New Jersey I helped build from scratch.
He gave me a copy, interesting stuff. He interested Isaac Asimov with that book and they became pen pals. It says among other things, you don't need a positive base to make a number system, it can be based on say, -15. Check it out, great little book! I just saw it on Amazon!

Originally posted by Aetherael
i know you were being cheeky, but i feel like this is an interesting point and would like to expound upon it!

you can make up whatever "symbols" you want, but the concept of the position system will remain the same - so rather than continuing the "letters and numbers" concept which eventually fails thanks to there being a finite number of "familiar" sym ...[text shortened]... ritten in base 49 as such:

[b](1,0;1,5) = 1*49^1 + 0*49^0 + 1*49^-1 + 5*49^-2[/b]

I may be missing something here, but it's just notation, right? Notation can and should be changed at will when that brings clarity to the operations.

Originally posted by gelareh
54 !

2.308 x 10^71

Originally posted by lausey
2.308 x 10^71

Near enough...

Originally posted by sonhouse
Have you ever heard of a book called "A number for your thoughts" by Malcom Lines?
It turns out he used to work at a start-up in New Jersey I helped build from scratch.
He gave me a copy, interesting stuff. He interested Isaac Asimov with that book and they became pen pals. It says among other things, you don't need a positive base to make a number system, it can be based on say, -15. Check it out, great little book! I just saw it on Amazon!

... and fractional bases?

for example base 1/2

5(decimal) = 1.01 (base 1/2)


Any practical applications I wonder?

Originally posted by lausey
2.308 x 10^71

I don,t understand this. Please explain 🙁

Originally posted by wolfgang59
... and fractional bases?

for example base 1/2

5(decimal) = 1.01 (base 1/2)


Any practical applications I wonder?

i think you may have miscalculated...

a fractional base of (1/n) would just map any number in base (n) to the right of the "decimal point" (i'm not really sure what the name of the place-defining syntax element would be called in a non-base 10 system - the "n-thimal point?" lol)

consider that n^(-x) = (1/n)^x

so 5(decimal) = 11 (base 2) = .11 (base 1/2)

similarly, 14.5(decimal) = 1110.1(base 2) = 1.0111 (base 1/2)

but this begs the question: are we allowed integer placeholders in a fractional base? in base 2 only the digits 1 and 0 are allowed... and it stands to reason that only 0 and 1 would be required to represent any number in base(1/2). similarly, in base (1/n) we could restrict the digits to the list 0,1,2,...,(n-1) but then isn't it more practical and internally consistent to just invert the order of our digits and move the "decimal point" to represent the number in base (n) without "breaking" any of the "rules"? food for thought 🙂

i haven't, you may notice, considered what would happen in a base of (x/n) which could prove to be much more interesting and less straightforward than (1/n)! though the same problem presents itself: what digits would be allowed, and would they be sufficient to have a unique representation of all numbers?

Originally posted by wolfgang59
I don,t understand this. Please explain 🙁

It's the factorial of 54.

Originally posted by Aetherael
i think you may have miscalculated...

a fractional base of (1/n) would just map any number in base (n) to the right of the "decimal point" (i'm not really sure what the name of the place-defining syntax element would be called in a non-base 10 system - the "n-thimal point?" lol)

consider that n^(-x) = (1/n)^x

so 5(decimal) = 11 (base 2) = .11 (ba ...[text shortened]... lowed, and would they be sufficient to have a unique representation of all numbers?

I was considering that the place values in any base x are;

x^2 x^1 x^0 (decimal point) x^-1 x^-2

which in decimal gives hundreds, tens, units, tenths, hundredths

extend to base 1/2 we get place values of

1/4 1/2 1 (point) 2 4

so that 1.01 in base 1/2 is 1+4 = 5

Originally posted by Palynka
It's the factorial of 54.

Thanks. I've had laser surgery on my eyes and everything is still a bit blurry. Especially !