0.999999… revisited

[Acer]

I hope I don’t bother anyone by asking this age old question again. Most of us are familiar (not so for me) with the problem of whether 0.999999… = 1 (I don’t agree). Is this problem similar for other bases? For example in hexdecimal does (0.FFFFFF…)(Base 16) = 1 or (0.FFFFFF)(Base 16) = 0.999999… Of course this can be extended to other bases.

A few observations to get this rolling:

1)
x = (0.FFFFFF…)(Base 16)
16x = (F.FFFFFF…)(Base 16)
16x – x = 15 x = (F)(Base 16)
x = 1

2)
0.999999… = (9/10) + (9/100) + (9/1000) +…
0.999999... = (9 / 10) / (1 – 1 / 10) = 1
(0.FFFFFF…)(Base 16) = (15/16) + (15/256) + (15/29696) + …
(0.FFFFFF…)(Base 16) = (15 / 16) / (1 – 1 / 16) = 1

(Or are they?…)

FYI, no, you’re not doing my homework

[Acer]

*mutters something about lack of maths font and subscript

[Zealot]

There have been a few threads about this in VSP. Here's one: http://www.greylabyrinth.com/Forums/Forum5/HTML/003800.html?119. It starts out with the 2=1 puzzle but by reply 15 turns into the .999... = 1 debate.

[mith]

*~polishes Sword of Mathematical Fact, or something~*

[CrystyB]

I washed my hands. Do with him as you wish! iow "FLAMES AWAY"!!!

[extropalopakettle]

To answer your question, yes, 0.fff... = 1 in base 16 (and similarly for other bases). Any other questions?

By the way, you say you don't agree that 0.999...=1, then you present weak arguments that they are equal. What's up with that?

"A few observations to get this rolling" ...

It rolleth not.

[Lilifreid]

Steals the Sword of Mathematical Fact

It will go wonderfully well with my Shield of Mathematical Induction.