Aralon ([info]aralon) wrote,
2005-07-15 14:10:00
  • Mood: contemplative

Query....

I have a question for all you math geeks out there. There are restrictions, though. Please read on.

I want to know your view on the great 0.999...=1 controversy. Using the simplest math possible. Without referencing other websites.

The reason I bring this to my community is because I really have no other venue to turn to. Most websites contradict themselves on the subject, or use math out of sequence to rig their conclusions.

I do have my own opinion, of course. I want to hear from other people before I share it, though.

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  • 15 comments

Anonymous

July 15 2005, 21:56:13 UTC 6 years ago

I think I can be considered a math geek but possibly not enough of one to really give a good conclusion. I'd say that it all has to do with limits. It took me a long time to accept limits and similar things in calculus yet there was a point where it really just clicked. I'd say that as you add another digit with the value of nine you get closer and closer to 1. therefore the limit as the number continues to gain digits of nine the next place out would be 1 because it is going to get so freaking close to one that it might as well be. I really hadn't heard much about it though so that's just my thought

:)

[info]dojcjfreak

July 15 2005, 21:57:50 UTC 6 years ago

I hate this new LJ system that I can make a response without even realizing that I wasn't logged in. The above attempts at genius were me :)

[info]aralon

July 15 2005, 22:03:34 UTC 6 years ago

Thank you....

I was wondering who might be anonymously trolling my LJ.

[info]dojcjfreak

July 15 2005, 23:19:38 UTC 6 years ago

Re: Thank you....

lol, yeah, I hope what I said made sense, I can try to be more clear if necessary but that's what I thought of off the top of my head

[info]aralon

July 15 2005, 22:02:49 UTC 6 years ago

I thouhgt of this....

However, there is always a number that can be expressed between 0.999... and 1. It would be typed out as 0.00...1. Actually, instead of the dots, there should be a line over the last zero. Also, this would be like saying that since the limit approaches one, the limit is one.

I know this is used for quite a bit of calculus, but it still seems an untrue postulate. A useful untruth, used to extract any small kernel of data from limited data points. But false nonetheless.

[info]dojcjfreak

July 15 2005, 23:24:31 UTC 6 years ago

I remembered to log in this time

Yeah, I think that's the way that it is, in calculus it is as good as true and like most other things with calculus, outside of the realm of calculus it really isn't when logically thought through. That's why I had so many issues with it to begin with.

Have you heard about how I think it was Liebnitz (maybe it was Newton) started doing derivatives? It was basically algebra only the added the (d/dx) bit to mean something so insignificant that it could be zero but it's not. Then he did algebra with it and any time there were two insignificantly small things multiplied together then that was so small that it could just be cancelled. We now have better ways of approaching calculus but seriously that's how they did it. I learned it in my History of Math class. I loved that class.

[info]ocicat

July 15 2005, 22:03:53 UTC 6 years ago

Using the simplest math possible:

.999... ~= 1

[info]aralon

July 15 2005, 22:25:03 UTC 6 years ago

Hmm..

Does that read as "approximately equals"?

[info]ocicat

July 15 2005, 22:30:22 UTC 6 years ago

Re: Hmm..

Yes.

[info]aralon

July 15 2005, 22:36:28 UTC 6 years ago

Okay.

I'm cool with that. 0.999... ~= 1.

[info]lady_equine

July 16 2005, 01:10:13 UTC 6 years ago

Re: Okay.

Yah, this is where I am.

I think that 0.999... ~= 1

And I don't sweat the details. But then, that's me. I had the worst time in geometry class, because I could clearly see the answer, yet they wanted me to prove it beyond saying "it just is". *grin*

Thanks [info]ocicat!

[info]dojcjfreak

July 16 2005, 04:03:24 UTC 6 years ago

Re: Okay.

Hey, because of proofs in geometry we are able to use hyperbolic geometry to do space travel. All because a bunch of people refused to believe that something plainly obvious was true.

[info]darkmane

July 15 2005, 23:49:21 UTC 6 years ago

I think the best way to express this is:

1-X = 1 where X approaches 0.

But while it's not true in a mathematical sense, the limit of the equation is 1-X = 1 as X approaches 0.

I don't see it as a contraversy but more as two different perceptions of the same thing.

[info]aralon

July 16 2005, 00:41:39 UTC 6 years ago

I think I get it...

I can now see it as the limit in that sense. I think I was given a poor definition for limits.

So while 0.999.../=1, 1 is the limit of 0.999..., due to never reaching 1.

The definition of limit I was given seems bad because it was based on there being no number between the infinite progression and the limit. Of course, there's always an infinitely small number between any number and the limit.

I think. ;p

[info]darkmane

July 16 2005, 01:27:10 UTC 6 years ago

Re: I think I get it...

The non-mathematical definition of a limit is the number that an equation approaches as a variable approaches a certain value.

The best example equation I can provide is a two part equation:

For x =1, y=2
for all other x y=1.

This is a valid, if silly equation. The limit of this equation as x approaches 1 is 1, because immediately either side of 1 (No matter how small you slice it) the equation equals 1.

Now, the limit of 0.99999\ is 0.99999\, not 1, no matter what value of X you plug into that equation it will always be 0.99999\. Limits of constants are always the value of the constant. And while probably an irrational number, it is a real number and always equal to itself.

Now, if you express 0.99999\ as y= 1-x, then as x approaches 0, y approaches 1 or lim(1-x) x->0 = 1.
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