Mathematic Fallacy

[Feared_1]

I know what an asymptote is, and you can't get one from .999... because .999... doesn't form a curve, it forms a straight line at y=1.
An asymptote is where a function does not exist... EVER. AHadley already brought up (1/x), for example. Because you can't divide by 0, the graph's domain will come from negative infinite and grow as the graph gets closer to 0. The range does shoot off into positive infinite and continues again from negative infinite, NEVER touching 0.

and AGAIN, .6' + .3' DOES NOT EQUAL .9' , it equals ONE.

You're saying exactly what I just proved but you don't believe.
.6' + .3' = .9'
.9999999... = 1
Therefore, using the transitive property, .6' + .3' = 1

Let me give you something else to chew on:
.33333333... = 1/3
If what you're saying is true, then the above is not true. .3333333... approaches 1/3, but never reaches it.
That's false. In fraction form, .3333333... is 1/3 EXACTLY.
In fraction form, .9999999... is 1 EXACTLY.

[Nielk1]

You're saying exactly what I just proved but you don't believe.
.6' + .3' = .9'
.9999999... = 1
Therefore, using the transitive property, .6' + .3' = 1

Let me give you something else to chew on:
.33333333... = 1/3
If what you're saying is true, then the above is not true. .3333333... approaches 1/3, but never reaches it.
That's false. In fraction form, .3333333... is 1/3 EXACTLY.
In fraction form, .9999999... is 1 EXACTLY.

No. 1/3 plus 2/3 is 3/3 or 1
0.3' + 0.6' again IS NOT 0.9'
0.3' + 0.6' = 1

I am NOT agreeing with anything you are saying. I am NOT applying the transitive property. It is simply that 0.9' is NOT the same number as 1. I think I would know after Calculus I, II, II, Statistics, Linear Algebra, and Discreet Math. Specifically Discreet Math.

EDIT:

1/3 is EXACTLY .3'
2/3 is EXACTLY .6'
3/3 is EXACTLY 1
0.9' is a mathematical fallacy on the part of the human. It does not occur. It is caused by assuming that two infinite decimals sum to another infinite decimal always. This is not the case. This would be like assuming that half of an even number is always an odd number.

Tell me when y=(-(1/x))+1 and .9' intersect?
I can tell you.
Infinity.
NOT UNDEFINED.
They intersect at in infinite distance, but they do intersect.
But if (-(1/x))+1 intersects a line that has no slope of any kind, and it itself never reaches 1, then neither can that line it intersects.
If that line was equal to 1, then the point of intersection would be undefined.

[Red Devil]

This is why calculus works.  Sooner or later, you split enough hairs to the point where it is moot.

[Feared_1]

I AM applying the transitive property because it is CORRECT. What part of my previous proof do you not understand?

.999... has INFINITE 9's at the end of it. INFINITE. You can't stop infinite! It is equal to 1.

http://en.wikipedia.org/wiki/.999

[Nielk1]

I AM applying the transitive property because it is CORRECT. What part of my previous proof do you not understand?

.999... has INFINITE 9's at the end of it. INFINITE. You can't stop infinite! It is equal to 1.

http://en.wikipedia.org/wiki/.999

No you cannot stop at infinity, you can only approach it... You should know this.

Well exxxxxxcuuuuuuse me for assuming we were using exact math and not using the "there are no nonzero infinitesimals" property. I find it interesting that Wikipedia (a bad source int he first place) still only notes when it comes to the pure mathematics that 0.999' ≈ 1, which I have no quarrel with.

In reality this all stems from the misunderstanding that 0.3' + 0.6' = 0.9', a common academic claim. As I have been saying all along, .3' + .6' = 1, not .9'. Thus there is no need to argue that .9' is = to 1. Claiming it is is simply the continuation of confusions and propaganda that has existed since calculators became commonplace.

Do note that you are summing two infinitely long decimals, think about that.

Maybe I should write this differently for you.

0.9' ≈ 1.0'

It is called an infinitesimal. You might want to ignore it, simple math may want to ignore it, but it is THERE.

I will now take the time to disprove some proofs to the contrary.

0.999... = 9/10 + 9/100 + 9/1000 + ...
and the sum of the geometric series on the right is
(9/10)/(1-1/10) = 1.

This is actually true, but the meaning of geometric series is misused. The series tells you what it approaches, but not always exactly what is is. Linguistic and mathematical trickery.

x = 0.999...
multiply both sides by 10
10x = 9.999...
subtract the first equation from the second
9x = 9
so
x = 1

This exploits the base 10 system, so let us do base 2.

x = 0.111...
multiply both sides by 10 (that is binary 2)
10x = 1.111...
subtract the first equation from the second
1x = 1
so
x = 1

So this also says that binary 0.1111 is the same as binary 1? 0.111 is just barely above 1.5 in decimal. Sounds suspicous to me.

I would also like to note how calculators work. They actually do limits and such, and decide what number a value fast approaches. This is why some calculators spit out .999 and others 1. It all depends on what extra programming they have on top and how far they plan to approach infinity in their calculation.

I will get some more later.

[Nielk1]

Looking at how ridiculous and frivolous this argument gets (as per my investigation of it on other sites) I think another so called mathematical fallacy should be brought up.

You should know better than to bring a massive forum flame-pile of a problem here...

[Feared_1]

Hmm, you're approaching this from a different direction than I am. You are using limits and I am plugging in "∞."
Because of this, we'll never really reach a conclusion... but oh well.
Sorry if my tone is overly critical, I don't mean to be intense, I'm just having a blast

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... = 1
Geometrically:
This isn't what we're talking about, but it's the same concept. Take a full square, split it in half. Split that half in half and you get a 4th, split the 4th in half and you get an 8th, split that in half and you get 1/16 and so on and so on FOREVER. If you do this for infinite (not a really big number), you end up with small bits and pieces of the full square. It is impossible to split it in half any longer after you have split it in half for infinite, even though it doesn't stop.

I'm not trying to analyze infinite by giving it a value. I have given up doing that. I am saying that infinite is forever and there is no valid attempt to analyze it any further.

Similarily, 1/2 * 2/3 * 3/4 * 4/5 * 5/6 * 6/7 * ... = 0
"..." doesn't mean go on for a super long time and find out what it approaches, it means do that for infinite without using limits. If you do do it forever, you WILL get 0 as an answer. It is impossible for humanity to do it, but that's what you'll get after forever.



EDIT: in response to your last post:
As far as I'm aware, we're not flaming. I choose not to jump into flame wars, and if it ever were to get there I would step out. I agree, there is no end to this argument (it goes for infinite ). It all depends on how you interpret the math and that's different for everyone.

[Nielk1]

The last 3 years of my math has been 'approaching' infinity and zero, you can understand why I have the view I do.

God I am sick of limits.

[Feared_1]

The last 3 years of my math has been 'approaching' infinity and zero, you can understand why I have the view I do.

God I am sick of limits.

I totally see your side of the argument. Your view is that "you can't get to infinite, so find the limit." That's valid math.
My view is "you can't get to infinite, but the 'limit x -> ∞' is the same answer as if you plugged in '∞' for x." Also valid math.

Basically, my view is "just give up" and yours is "don't even try." All depends on how you interpret things.

[Steeveeo]

AHadely, you should be ashamed of the mess you created!

[mrtwosheds]

If you do do it forever, you WILL get 0 as an answer.

Hmm no. The Universe is made of something and nothing. Non zero +numbers represent the something, zero represents the nothing. 0 is infinite in its non-existence, no amount of multiplying will alter that state at all, equally no breakdown of non a zero number will result in 0.
0 is not a number, it is the "paper" on which all other numbers or things are written.

Mathematics must represent the Universe that allows it to exist, otherwise it is just nonsense.
So next time you do a calculation that ends up with a - answer, ask yourself how that is possible.

[ScarleTomato]

the base (get it? heheh) problem i think is that you usually don't do proofs with repeating decimals anyways, because by definition they are so inaccurate. Usually you stick to the fraction because they're absolutely precise.

[Feared_1]

So next time you do a calculation that ends up with a - answer, ask yourself how that is possible.

Instead of giving it for me to do, you should do it yourself!

I'll do it this time...
1/2 = 1/2
1/2 * 2/3 = 1/3
1/2 * 2/3 * 3/4 = 1/4
1/2 * 2/3 * 3/4 * 4/5 * 5/6 * 6/7 * 7/8 * 8/9 * 9/10 = 1/10
1/2 * 2/3 * ... * 29/30 = 1/30
1/2 * 2/3 * ... * 99/100 = 1/100
1/2 * 2/3 * ... * 999999/1000000 = 1/1000000
1/2 * 2/3 * ...forever = 0
Where x is the product.

If I were to use a limit:
lim(x -> ∞) = 0
The longer I go, the closer the answer gets to 0. If it goes on forever (which is not humanly possible), the answer you get will be 0.

ask yourself how that is possible.

It's not possible for humanity, but mathematically it is because math can do infinite.

I understand that you're confused. Try to stop trying to give infinite a number value and just accept the fact that it is never-ending and it will become MUCH easier.

[sabrebattletank]

Basically, my view is "just give up" and yours is "don't even try." All depends on how you interpret things.

No, "don't even try" is MY view.

[Feared_1]

I was talking to Nielk1 in that post.