Is 0.99999 = 1?

De-Gen · #1 25-01-2006, 03:37 PM

Let X = 0.99999...

10X = 9.99999...
10X - X = 9.99999... - 0.99999...
9X = 9

X = 1

[1ponders] (Paul) · #2 25-01-2006, 03:41 PM

I don't know why, but no

De-Gen · #3 25-01-2006, 03:42 PM

yep, that is strange...

ving (David) · #4 25-01-2006, 03:43 PM

by rights it shouldnt be

[1ponders] (Paul) · #5 25-01-2006, 03:44 PM

Somewhere along the line you are going to have 0.000.........ad infinitum....0001 left over in your subtraction wont you

ving (David) · #6 25-01-2006, 03:45 PM

one again, let X = .99999

10X = 9.9999
X/10 = .09999

therefore X = frog

Thiink · #7 25-01-2006, 04:08 PM

If I showed this thread to some of my friends, they would instantly groan and roll their eyes

.

For almost the whole of year12 (and various flare ups since) this debate (well similar) would come up. The argument for us was if 1/3 = 0.333(repeater), does 0.333(repeater) x 3 = 1, or 0.999(repeater). Half said its 1, the other half (including me) said it was 0.999(repeater).

Whats the point of the word 'infinity' if people always just assume repeated infinite values are whole numbers?

avandonk · #8 25-01-2006, 04:30 PM

You are discussing whether you know it or not "What is the smallest real physical bit in the Universe?"

Currently anything smaller than the Planck length is indefinable.(1.6X10^-33cm)

There is no answer to your question as a mere mechanical/electronic device can not answer questions any deeper than the question put to it. It is an automaton.

Use the necktop that you were born with to work this out.

The best computer you will ever own is the one between your ears!

Bert

ving (David) · #9 25-01-2006, 04:42 PM

/me searches for computer between my ears.....

hmm...

avandonk · #10 25-01-2006, 05:17 PM

The real answer is all computers are limited to the number of bits they work at;

eg 8bit = 2^8= 256

16 bit = 2^16
32 bit = 2^32

All the protocols for simple arithmetic computation take account of rounding errors.
You have found one.

Bert

acropolite (Phil) · #11 25-01-2006, 05:25 PM

Limit the number of decimal places and it doesn't work.

X=.99999
10X=9.9999
10X-X=8.9991
therefore 9X=8.9991

.99999 recurring is not an exact number but depending on how many decimal places you take it gets closer to 1 but never 1.

janoskiss (Steve H) · #12 25-01-2006, 05:50 PM

My tolerance for these sorts of discussions has its limits.

stinky · #13 25-01-2006, 05:53 PM

Simple test to find out if it's 1
1 squared = 1

Sorry 0.999999999999999999999999999999999 99999999999999999999999999999999
x 0.999999999999999999999999999999999 99999999999999999999999999999999

can never = 1, in fact it just takes it further away!

janoskiss (Steve H) · #14 25-01-2006, 06:02 PM

Quote:

Originally Posted by Thiink

...
Half said its 1, the other half (including me) said it was 0.999(repeater).

So why not just split the difference?

bird (Anthony Wesley) · #15 25-01-2006, 06:04 PM

Quote:

Originally Posted by avandonk

You are discussing whether you know it or not "What is the smallest real physical bit in the Universe?"

Currently anything smaller than the Planck length is indefinable.(1.6X10^-33cm)
Bert

Bert, the question here is pure mathematics question, doesn't really have any relation to the physical universe. It's quite easy to write down or do arithmetic with numbers smaller than the planck constant :-)

I think the issue here is that 9.999... and 0.999... are both non-rational numbers, and do not obey the normal rules of arithmetic, so it's invalid to subtract them like that.

regards, Bird

stinky · #16 25-01-2006, 06:35 PM

Besides not being sqareable you can't deal with absolute and approximate values in the same equation,

That's why Pi 3.142597............ will only ever be an approximation but 22/7 is exact.

Get back to the precise imperial system!

bird (Anthony Wesley) · #17 25-01-2006, 09:09 PM

Quote:

Originally Posted by stinky

Besides not being sqareable you can't deal with absolute and approximate values in the same equation,

That's why Pi 3.142597............ will only ever be an approximation but 22/7 is exact.

Get back to the precise imperial system!

I hope I'm not reading you the wrong way, but PI is 3.14159...etc, not 22/7. Im sure you weren't saying that, but your post was a little ambiguous, some people may have read that as saying PI is exactly 22/7.

PI is not rational, so cant be expressed as x/y for any integers x and y.

regards, Bird

Sausageman (Mike Boggan) · #18 25-01-2006, 09:21 PM

Will you guy's stop it, I'm getting a headache.

Mike

Greg Bryant · #19 25-01-2006, 09:54 PM

A Maths teacher at school back in the 80s (must have been in the NSW curriculum!) showed it to us this way

1/9 = 0.111111 (repeater)
8/9 = 0.888888 (repeater)

1/9 + 8/9 = 1

Therefore, what does 0.111111 (repeater) + 0.888888 (repeater) =?

Still, this same teacher in 1986 let me skip class to go to the School Library to watch the live images of Giotto's flyby of comet Halley. When I returned to class, he asked me to describe the results to the class - as I did, he sketched the whole flyby on the blackboard.

DRCORTEX (Lance) · #20 25-01-2006, 10:09 PM

And perhaps that is why you do what you do, so well, and more importantly - enjoy it

ciao

Lance