(no subject)

[theducks]

Here's an interesting article that postulates that .999 recurring = 1.

For those of you on my friends list who don't have a PhD in Mathematics, and the one of you who does but in an unrelated field.. the ideal is that since 1/3 = .333 recurring, and 2/3 = .666 recurring, and .333 + .666 = .999 and 1/3 + 2/3 = 3/3 = 1, .999 and 1 are the same number. The proof is further suggested by the fact that if .999 is less than 1, how much less? an infinate number of 0's, followed by a single one? :)

It's a cute read. For many purposes, .999 does equal one, but in other terms, it's like saying π = 4

Comments

[dannipenguin.livejournal.com]

I dislike the conclusions you have drawn in the face of no references to number theory.

If you don't follow the idea of the geometric sum to infinity and so on, you are better off considering 0.9 recurring as 1^-. That is, the non-descript instant before whatever happens at '1' happens. In electronics, this might be the very instant before the switch is flicked, in calculus this might be the value of a limit approaching the left-hand side of a discontinuous point.

You must also be aware that all measured data can only be read to a certain number of significant digits and further calculations on this data cannot have more significant digits than the measured answer. Thus, if you calculate 0.9999, but your most accurate measurement is only to 3 significant figures, the answer is 1.00 (you have to round up).

[theducks.livejournal.com]

I'm fox news buddy. I make no conclusions, I just report this guy's :)

[ataxi.livejournal.com]

0.9 recurring is equal to 1, for the same reason that lim (n --> inf) 1/n is equal to 0. In my understanding the expression "0.9 recurring" describes a limit process that converges on 1.

You might be interested to know that the real numbers are defined this way anyway (i.e. one represents real numbers as the set of "Cauchy" rational sequences - sequences of rational numbers in which the terms get arbitrarily close together - and the irrational numbers are then those such sequences which are Cauchy but do not converge to a rational number).

Haven't read the link, but I'll go to my grave swearing "but Officer, 0.9 recurring IS 1!" :-)

[dannipenguin.livejournal.com]

Yeah. I reasoned it out with limits after I went to bed. I figured it wasn't worth getting up to post again ;)

My reasoning went a number smaller than 1 is (1-1/n) so a number infinitesimly smaller than 1 is lim (n->inf) (1 - 1/n), break apart by the linearity property and you end up 1 - 0 (from the limit you gave above).

[ataxi.livejournal.com]

Oh yeah, I would also claim this is a problem of "analysis" not "number theory".

[oliverm.livejournal.com]

Not that it's like me to be pedantic but....

Firstly, the article doesn't postulate that 0.999 recurring = 1, it proves it (which is a significant difference)

Secondly, 0.999 does not equal 1, 0.999 recurring does equal 1. This may be a typo on your part, but it is important. From a mathematical standpoint saying that 0.999 = 1 is as valid as saying that -12 = 10,000,000,000 (although for practical purposes I admit it is quite different)

The later parts of the proof are really not required, they are just an attempt to get non-mathematical people to realise the truth, that 0.999 recurring does equal 1. The argument that they are written differently is completely irrelevant, as an example consider 0.5 and 1/2 Would anyone argue that they are not equal? I doubt it.

If you do want to question the proof, I suggest finding anyone, anywhere, who has any evidence that 0.999 recurring does not equal 1

[david adam <zanchey> (from livejournal.com)]

But you're a mathematician! Surely you aren't supposed to make such grave logical errors as in yur last sentence!

[david adam <zanchey> (from livejournal.com)]

(I blame lag for the spelling error. Editing in Firefox is a process with latency, damnit.)

[oliverm.livejournal.com]

Apologies, I should of course have asked if anyone wanted to question the premise, not the proof.

[ataxi.livejournal.com]

Although in general if someone says "0.9 recurring doesn't equal 1" the response "what's the difference then?" should beat them down quite quickly :-)

[theducks.livejournal.com]

It *is* a typo/laziness. I was meaning .9 recurring for every instance of .999 (likewise .3 recurring and .6 recurring).. I'd have put a bar above it, but I have no idea how to do that with HTML :P

I could have been clearer I suppose, but c'mon, I did do TEE maths, I know that 1/3 = .3 recurring and not .3330 :)

And yes, you're right, it is a proof not a postulation.

[alias_sqbr]

I remember being quite vocal about the fact that 0.9 recurring was not equal to one in primary school, then being kind of convinced they're the same in highschool, then learning proper calculus etc at uni and going "FINE, they are the same". For the reasons Oliver and Tom said :)

[greteldragon.livejournal.com]

I remember this debate happenning in unisfa a while ago where it was Adrian Orlando on one side, and everyone that had studyed maths on the other. I think Adrian won through all the mathematicians giving up in digust or boredom. It went over about two days. :P

[paperishcup.livejournal.com]

Oooh that was cool. I miss maths (well, kind of). And the article was way more interesting than the essay I'm currently writing (which, incidentally, is due in an hour...eek!).

Glad to hear you and Liz are having fun (go Singapore Airlines!). Universe is still standing and intact (and sparklingly clean...thank you!!!), and is being treated it with the utmost respect. Spare bedroom is now my study and network as you can see is working fine. And I'm practicing admirable amounts of restraint at not yet delving into the wealth of dvds you have that I'm desperate to watch!

Enjoy the rest of Singapore...I hear the zoo is spectacular...

[infamyanonymous.livejournal.com]

Now that's the kind of maths that makes sense to me :)