from the artist's etsy link:

Depends on the baby, apparently. $15 plus $4.95 shipping.

But I'm not a baby!

You've got to be somebody's baby.

Or, find a baby with a head the same size as yours, order the beanie for the baby, but trade candy for the beanie when the hat comes in the mail. That should be easy.

Plus, the artist doesn't say she needs a baby, she needs a size. Certainly you have a size, don't you?

and stare in wonderment at its mother!

This has been messing with my head for some time.

(i'm having trouble with the notation. I'll write r to mean recurring last digit.)

okay, the argument is:

1/9 = .1r
2/9 = .2r
3/9 = .3r
etc
8/9 = .8r
so
9/9 = .9r
But since any x/x = 1
9/9 = 1
hence .9r = 1

Hmm. Troubling.

Intuitive reply.
No it bloody doesn't. See, this is 1. It starts with a 1. That over there is 0.9r. It starts with either a zero or a nine, depending, but either way, it is different from 1. Any fool can see that.

Think of the number line. Zero in the middle, negatives off to the left, positives off to the right. .9r would be immediately to the left of 1. We zoom in, closer and closer; .9r is always abutting 1 on 1's left, but never quite in the same place. Keep zooming, it is always there.

Okay, that's not very convincing if you weren't already convinced.

Here's a better counter argument.

0.9 < 1
0.99 < 1
0.999 < 1
0.9999 < 1

etc

0.999999999999999999999999999999999999999999999 < 1

Observation: adding more nines does not change the fact that it is less than one, no matter how many you add.

so,

0.9r < 1.

Hence, 0.9r =/= 1.

So, apparently, 0.9 both is and is not equal to one.

Man, I think we just accidentally the whole mathematics. Or my head.

By coincidence, I added the explanation to my sig line just a day or so ago while exploring IM's thread on Number Associations.

x ≠ y ⇔ ! (x = y)

See, kings can work together !:rolleyes:

Hi Zen,

If 0.̅9̅ were not equal to 1, there would have to be a difference d.

For any value d you can find an exponent n, so that 1/10^(n) >= d > 1/10^(n+1)

e.g. d = 0.0002
0.001 >= d > 0.0001

But if that value d were the difference, then it is obvious that

(1 - d) < 1 - 10^(n+1) < 0.̅9̅

e.g. 0.9998 < 0.9999 < 0.̅9̅

So, obviously the difference is less than d=0.0002 or any d you choose.

:3_eyes: :D

http://en.wikipedia.org/wiki/0.999...

How can you tell they're not in the same place? There's no space between them. No matter how much you zoom in, that space will never open up.Infinity is different. For example:
No matter how many finite numbers you add together, you will never reach infinity - unless you add an infinite number of numbers.
Likewise, no matter how many nines you add to 0.9999..., you will never reach one - unless you add an infinite number of nines.
That's the page I tried to copy-and-paste the proper barred number from.

I think you'll have to subtract a finite number of decimal points to ever get to 1.

'Sall I know. 'Sall I'm sayin'.

Attachment 37552

I don't understand. Subtract decimal points?

So, assuming that it is not merely a phone that looks like a mouse, or a mouse that looks like a phone (much like the mouses that look like mice or eight balls), I presume that like many hybrid devices, it does neither duty well.

I opened the page and just saw Wolf's post.
How disappointing to scroll up and see it's that kind of mouse.

robotic kitchen:
http://www.youtube.com/watch?v=lFEX5zNvP9M

it's like doing all the work of being in the kitchen without the sense of smell telling you what to add and how much...