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Forums - General - 0.9999.... = 1.0

 

Are you convinced?

Yes 34 58.62%
 
No 20 34.48%
 
not sure 1 1.72%
 
Total:55
dsgrue3 said:
Jay520 said:

This is a fairly old topic so I'm not sure if all of you have heard about this. I just found out about it and found it interesting.

The claim is that 0.9999.....(infinite 9s) is equal to 1.

Here are some proofs

-

x = 0.9999… given
10x = 9.9999…. multiply by 10
9x = 9 subtract x
x = 1 divide by 9
0.999... = 1 substitution

 

You went from 10x = 9.9999... and by subtracting x somehow arrived on 9x = 9; this is wrong. You should have arrived on 9.000.....1x = 9.

Series will converge to 1, but never arrive at it. It's like saying that you can divide 1 in half and eventually get to 0. You can't. You can approach 0, but never reach it. 

As to 1+1 =3 for sufficiently large values of 1, it's just a joke. 1.49 +1.49 = 2.98.

Once you add percision to that. He using a percison of 1., which technically will not work either. Because you usually round to the percision before adding anyways. I got into an argument with a friend of mine about this. Yes you can do it the way he wants to and end up with 3. But it not proper technique, with Percision and Accuracy both going out the window. The correct technique is the way you did it.



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Conegamer said:
This is great! More Maths!

But I thought what Jay said was a known truth. So why the arguments?

Now if you want difficulty, try explaining how any irrational number contains every possible ordering of numbers (so in JPEG form every single picture that has, and will, ever be taken), how ever snowflake is unique or how a fractal has an infinite perimeter but a finite area...

This is not true for every irrational number, it is very simple to write down irrational numbers that do not contain any instance of the digit '5'.  However the vast majority (in the sense of Lebesgue measure) of real numbers are normal, meaning that they contain every finite string of digits with the same asymptotic frequency as a uniformly random distribution.

In addition I forgot to mention that with compound interest, you will never get more than e times the amount you started off with, proving Futurama to be invalid.

Utterly false, sloppy reasoning.  You're just thinking the limit of compounding on decreasing time scales which converges to continuous compounding.  If you really think this is true, won't you let me loan you a penny with 0.1% interest per second compounded?

The Futuruma writers have way stronger math backgrounds than the vast majority of the people in this thread, not that they were being serious all the time...This thread is almost as depressing (in terms of demonstrating the failure of education) as those pseudomath posts on Facebook which get 100 wrong answers for every right one.



Not to sound arrogant, but it's a pretty established fact that 0.999.. equals 1.



Soleron said:
MDMAlliance said:

...


I said "proofs" as in math proofs.  Equations that show the work.  

Nothing in this thread is a math proof.

However, .9 repeating only represents 1 as applied to the real world due to the fact that .9 repeating does not exist as a number.  

"Existing" doesn't come into it. It represents the same object as 1.

It's the same thing as not being able to use infinity as a number in your equation, because it isn't.

Infinities are treated very differently in pure maths. They can be used correctly if you know what you're doing.

 Also, if we say an object cannot get any bigger than a certain size and no smaller than a certain size, 1/3 will not actually equal .3 repeating infinitely.  It would go to a point where it actually ends.

You're still imagining real "things" which must have a finite extent. Something going on infinitely in that representation doesn't automatically disqualify it. I mean, with maths you can take apart a sphere and reassemble it into two spheres of equal size with no logical contradiction. It's physically impossible but perfectly correct.



Well, it is perfectly correct once you accept the axiom of choice, as far as I remember. That's not exactly a good argument in this discussion.



Talal said:

Not to sound arrogant, but it's a pretty established fact that 0.999.. equals 1.


I think we're using the word "fact" wrong if it is contested.  In pretty much any math equation you will ever come by, it will equal 1.  However, it is not a fact that .999... itself is actually 1.  Every time I see someone trying to prove it, it keeps showing me that they are either using circular logic, or are approximating, then claiming they are the same thing.



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infinite is not a number therefore it doesnt exist



Tsubasa Ozora

Keiner kann ihn bremsen, keiner macht ihm was vor. Immer der richtige Schuss, immer zur richtigen Zeit. Superfussball, Fairer Fussball. Er ist unser Torschützenkönig und Held.

AbbathTheGrim said:

Ok, so let me get this straight, if we apply this rule to actual daily life, if a man feels like a woman, behaves like a woman and looks like a woman but still is missing a vagina that still makes him 1 woman.

The things which make a woman to a woman are finite so that example is not a good one, especially since you mentioned feelings, behaviour and looks, which are subjective anyway. According to your logic a woman who likes to watch Hockey, American Football etc. or has her head shaved (ignoring cancer) is a man and not a woman, even though she would still be a lot closer to the value 1 (which you define as woman), than any man could ever become.



kljesta64 said:
infinite is not a number therefore it doesnt exist


You cannot draw a circle, so it doesn't exist.

I never met you in the real world, so you don't exist.

 

 

Some of you are still not making the difference between a mathematical object and the way we represent it. It's not because we cannot write a number that it doesn't exist. For example, you cannot write the number of particles in the whole universe (which is finite) but this number still exists!



Jaydi said:
kljesta64 said:
infinite is not a number therefore it doesnt exist


You cannot draw a circle, so it doesn't exist.

I never met you in the real world, so you don't exist.

 

 

Some of you are still not making the difference between a mathematical object and the way we represent it. It's not because we cannot write a number that it doesn't exist. For example, you cannot write the number of particles in the whole universe (which is finite) but this number still exists!


in theory yes I do not exist if you dont see me...and if there is an infite amount of parallel universes then there is an infinite amount of particles..so if theres an infinite amount of particles,atoms etc...does this then mean we do not exist. mindblowing :*D



Tsubasa Ozora

Keiner kann ihn bremsen, keiner macht ihm was vor. Immer der richtige Schuss, immer zur richtigen Zeit. Superfussball, Fairer Fussball. Er ist unser Torschützenkönig und Held.

Barozi said:
AbbathTheGrim said:

Ok, so let me get this straight, if we apply this rule to actual daily life, if a man feels like a woman, behaves like a woman and looks like a woman but still is missing a vagina that still makes him 1 woman.

The things which make a woman to a woman are finite so that example is not a good one, especially since you mentioned feelings, behaviour and looks, which are subjective anyway. According to your logic a woman who likes to watch Hockey, American Football etc. or has her head shaved (ignoring cancer) is a man and not a woman, even though she would still be a lot closer to the value 1 (which you define as woman), than any man could ever become.

Nope, cuz a woman can watch Hockey, American Football and be bald womanly.



Nintendo is selling their IPs to Microsoft and this is true because:

http://gamrconnect.vgchartz.com/thread.php?id=221391&page=1