If 0.999 (etc.) = 1, does 1 - 0.999 = 0?

[Violet Lilly Blossom]

(4th March 2012 22:57)Child of Stardust Wrote:  Naw, but you see, there are other circular things. What about Cherrios? Fruit Loops? There are lots of DVD's and mood rings too but I think they are somewhat less numerous, though they may have the last laugh since they're not biodegradable.

Then they, alongside their doughnut masters, are winning! ARE YOU OKAY WITH THIS?! ARE YOU GONNA LET THAT HAPPEN?!

Quote:So I think there will be a cereal alliance against the doughnuts, which will result in a fight to the death where the Cheerios would swarm the donuts by sticking to them, thereby suffocating them and killing them all. After that it would be an epic three way battle between Apple Jacks, Cheerios, and Fruit Loops (and any other types of O-shaped cereal I've forgotten, but the Cheerios' sheer numbers will ensure they will emerge victorious).

Don't be ridiculous, round foods of all sorts (even spherical ones) work for the doughnuts. Doughnuts are the masters of all delicious roundness and will rain their sweetness upon us all!

THE STICKY END IS COMING!

[Categories+Sheaves]

There's a mountain of tacit assumptions being made when we write an infinite decimal. If you take a course in real analysis, you'll learn what that business is. But until then...

The main issue is that what you're thinking of when you write 1 - 0.999..., if this quantity isn't zero, is something that we can't represent with a decimal. I'm sure you've seen the "proof" about how 1/3 = 0.333... implies 1 = 3*(1/3) = 3*(0.333...) = 0.999...
That reasoning should be sufficient.

[Violet Lilly Blossom]

Did I ever mention that I love MLP: FIM?

[Categories+Sheaves]

(4th March 2012 23:10)Vaeolet Lilly Blossom Wrote:  Did I ever mention that I love MLP: FIM?

I figured, given the rep adjustment you gave me.
Also: that song is pure happiness. If Rainbow Dash hadn't struck such a thoughtful pose, I would be using a Pinkie Pie avatar. Because Pinkie Pie is best pony. (Also: Dashie Pie is the best main character shipping)

[Child of Stardust]

(4th March 2012 23:08)Categories+Sheaves Wrote:  The main issue is that what you're thinking of when you write 1 - 0.999..., if this quantity isn't zero, is something that we can't represent with a decimal.

Yeah, that's true. Why does this necessarily need to be a problem though?

Quote:I'm sure you've seen the "proof" about how 1/3 = 0.333... implies 1 = 3*(1/3) = 3*(0.333...) = 0.999...
That reasoning should be sufficient.

Does 3.333* = 9.999* then? I know it comes out that way on the calulator but I thought that was just because we don't have room to write out the infinite 3's, nor is the caculator capbable of calculating infinity.

If that's true that makes sense then. I haven't come across that proof yet...the 9.999 = 1 thread was split up and I didn't read the first half of it. Or maybe I just skimmed over it in the other thread. Anywho, thanks for the clarification.

[Cogitantis]

(6th March 2012 06:33)Child of Stardust Wrote:  Does 3.333* = 9.999* then?

Typo I guess, perhaps you meant 3*(3.333...) = 9.999...? In that case: yes, correct.

By the way, it's usually better to use '...' to indicate infinitely repetitive decimals, rather than '*' cause the latter also means multiplication. Sometimes a notation like 0.9 is also used, for example 7/12 = 0.583 (meaning 0.583333333...)

You can also have more repetitive decimals, e.g. 2113/2475 = 0.8537 = 0.8537373737...

[Child of Stardust]

(6th March 2012 15:27)Cogitantis Wrote:  

(6th March 2012 06:33)Child of Stardust Wrote:  Does 3.333* = 9.999* then?

Typo I guess, perhaps you meant 3*(3.333...) = 9.999...? In that case: yes, correct.

Mybadz, that's what I meant. Thanks.