Is blizzard up to something ? Opinions needed

[Goldenavatar]

Blizzard should stop to do some weird maths, and go on with game developping :lol: ! They call *that* a proof ?? The main point of the proof is how they define "...", and that's precisely what they "forgot" to do :lol: ! Btw, the first formula is right (the magic word is "lim"), but below that, the way to prove it is crappy !

I remember reading a bunch of responses to this .9 repeating topic a while ago. Having a Masters degree in math (MSU 2001) it was funny to read all the people saying that the whole thing is wrong. Where do people get their bogus opinions? Let's put the whole topic to rest.

0.9 repeating DOES EQUAL 1!

And there's NOTHING crappy about the way they show it. Limit is NOT needed to establish this fact. Just because you can use infinite series ideas from calculus to prove the statement DOES NOT mean other arguments are wrong. The method demonstrated by Bliz is COMPLETELY valid, is well established, and may be used to convert ANY repeating decimal to a fraction. But we can be even faster than that. No one denies that
1/3=.3333333...

Now multiply both sides by 3. Done.

 

[Frosty_The_Snowman]

Yes, but...

I remember reading a bunch of responses to this .9 repeating topic a while ago. Having a Masters degree in math (MSU 2001) it was funny to read all the people saying that the whole thing is wrong. Where do people get their bogus opinions? Let's put the whole topic to rest.

0.9 repeating DOES EQUAL 1!

And there's NOTHING crappy about the way they show it. Limit is NOT needed to establish this fact. Just because you can use infinite series ideas from calculus to prove the statement DOES NOT mean other arguments are wrong. The method demonstrated by Bliz is COMPLETELY valid, is well established, and may be used to convert ANY repeating decimal to a fraction. But we can be even faster than that. No one denies that
1/3=.3333333...

Now multiply both sides by 3. Done.

Well, I won't go too deeply into details. Try googling a bit and you'll find some serious demonstrations. This topic has been discussed on many forums.

But first of all, don't let me be misunderstood :
I've always agreed to say that the infinite serie sum(n=1, infinite) 9*10^(-n) tends to 1.
[HIGHLIGHT]Blizzard is right with the result, not with the demonstration.[/HIGHLIGHT]

The only thing I say in my post is that the "simplified" (childish) notation of this formula ("0.99999... = 1") has been unproperly proved by Bilzzard (i.e. in a non-mathematical way).

Here are some hints :
- How do they define "9 * ..." ?
- What is "..." ?
- How do they define 9.999... - 0.999... ?

The definition of "..." is the keypoint of the demonstration.

A bad manipulation of the limits can lead to a random conclusion. I'll give an example to prove that I'm definitely right :

[HIGHLIGHT]I'll prove that 1+2+4+8+16+... = -1 using the same arguments than Blizzard[/HIGHLIGHT].

A = 1+2+4+8+16+...
A = 1 + 2*(1+2+4+8+16+...)
A = 1+2*A
A = -1
Done .

I think the flaw in my "demonstration" can be understood by anyone after 1 year of mathematics in the University. That's why I'm very surprised that with your diploma, you can't see the flaw in Blizzard's demonstration. They're just lucky with their conclusion, but they don't prove anything mathematically. Just remember that I've used the same method as Blizzard, and I've produced an example to the contrary. And you'll soon find out that the underlying reason is a bad manipulation of... limits .

Tip : Blizzard finds the right result because 9.999... and 0.999... tend to finite values (10 and 1) so 9.999... - 0.999... has a "sense" mathematically. But my demonstration is false because of the operation "infinite - infinite value".

- Frosty

 

[Punkonjunk]

OK, so now we're debating it? Yes it equals one. Cool, blizzard.

Lets not get too hyped... I got hyped for 1.11b and look what we saw. :/

It's pretty neat anyhow, though.

 

[theredpredator]

A = 1+2+4+8+16+...
A = 1 + 2*(1+2+4+8+16+...)
A = 1+2*A
A = -1
D
[/I]
- Frosty

U cant say that... same as (1+2+4+8+16+..)= 1+2*(1+2+4+8+16+..)
That is incorrect at that stage. it should be a=1+2*B

As for blizzards explanation, 1=0.999, putting 1 as x. multiply both sides by 10, equals 10x=0.99999, 10x-1x=9.999-0.99 -> x=1.

a= 1+ 2*(1+2+4+8+16+..) multiplybu ten
10a = 10+(2*1+2+4+8+16..)*10
10a-1a=10-1 (2*(1+2+4+8+16))*(10-1)
9a=9*(2*(1+2+4+8+16..))*9
a= 1*2(1+2+4+8+16..)

Im tired now.. :xmas15:

 

[Frosty_The_Snowman]

U cant say that... same as (1+2+4+8+16+..)= 1+2*(1+2+4+8+16+..)
That is incorrect at that stage. it should be a=1+2*B

No no, it is perfectly correct to write A = 1+2*A with A = Sum(n=0, infinite) 2^n

The flaw is on the next step : 2A - A = -1, because A tends to infinite, so the result of "infinite - infinite" isn't defined.

 

[theredpredator]

No no, it is perfectly correct to write A = 1+2*A with A = Sum(n=0, infinite) 2^n
.

No its wrong :xmas17: n aint 0 coz if it is 0 a is 0. -0=1? define n? How much u value n? mal?

respetc

 

[AnimeCraze]

No no, it is perfectly correct to write A = 1+2*A with A = Sum(n=0, infinite) 2^n

The step is indeed valid. n is just the dummy summation variable, just like x when you do finite integrals. The next step is not valid since A does not converge. Series manipulation, absolute convergence, etc...... I am tired too.

For example:
sum (n=0, 5) 2^n = 1 + 2 + 4 + 8 + 16 + 32. n does not appear in the actual expression.

 

[Punkonjunk]

OK seriously, this isn't supposed to be a flame. but...

WHO FREAKING CARES? Blizzard already had this debate back at there forums.
They obviously have reached a conclusion. Why should we fight over that conclusion?
A WRONG STEP IN A METHOD REACHING THE SAME ANSWER STILL YEILDING THE CORRECT ANSWER MAKES THE FACT THAT IT IS WRONG POINTLESS TO DEBATE. I know this same formula couldn't be applied to other things, but hey.

 

[AnimeCraze]

A WRONG STEP IN A METHOD REACHING THE SAME ANSWER STILL YEILDING THE CORRECT ANSWER MAKES THE FACT THAT IT IS WRONG POINTLESS TO DEBATE.

That would net you a 0/10 on a Putnam problem, congraduations. To mathematicians, the method (ie. proof) is the most important, NOT the answer. We are not engineers......

Edit: If you don't care, don't read it :xmas9:

 

[stkrause]

A WRONG STEP IN A METHOD REACHING THE SAME ANSWER STILL YEILDING THE CORRECT ANSWER MAKES THE FACT THAT IT IS WRONG POINTLESS TO DEBATE.

You obviously never debated much with mathematicans, did you? :xmas17:

*stkrause

(and Frosty is right )

edit: Hey Frosty, welcome back :xmas21:

 

[Punkonjunk]

I know, and I've done proofs, sorry if I look retarded on that one. I'm just saying, they got the right answer on this one, with a bad method. I cared for a little bit, and when I read the thread on Bnet forums. It seems kinda pointless to debate the same thing they just finished debating. :xmas23:

 

[Frosty_The_Snowman]

Now you may wonder why I've grabbed back this old thread.
Well it's a funny story : as you probably know now, I've been out for around a month and a half, because I was very busy preparing my removal to the other side of the country, looking for a new job, a new apartment, and so on... Anyway, I've lost my bookmarks inbetween, and thus in order to find back the forum's URL quickly, I've googled a bit with "frosty_the_snowman diabloii" as keywords. And the first answer Google gives is precisely this old post. By opening it, I saw I had an (old) answer from Goldenavatar, and I felt like I had to answer it :xmas26:.

:xmas31: :xmas5: :xmas27: (OMG I love those new smilies !)

 

[rykuss]

Well i can't argue with any of that because i have no flippin' idea what all that means. Just wanted to say welcome back frosty! :xmas6:

 

[krischan]

Here are some hints :
- How do they define "9 * ..." ?
- What is "..." ?
- How do they define 9.999... - 0.999... ?

The definition of "..." is the keypoint of the demonstration.

A bad manipulation of the limits can lead to a random conclusion. I'll give an example to prove that I'm definitely right :

[HIGHLIGHT]I'll prove that 1+2+4+8+16+... = -1 using the same arguments than Blizzard[/HIGHLIGHT].

A = 1+2+4+8+16+...
A = 1 + 2*(1+2+4+8+16+...)
A = 1+2*A
A = -1
Done .

Blizzard defined 0.999~ or 0.999... in a way it's generally accepted, as the limes of an infinite sum of numbers. However, they forget to prove first that this limes is finite (which you - purposely - skipped as well) before doing things with it which can only be made with finite values, In any case, you can prove that for their limes (expressing 0.9+0.09+0.009+...) while you will fail with 1+2+4+...

 

[Frosty_The_Snowman]

Blizzard defined 0.999~ or 0.999... in a way it's generally accepted, as the limes of an infinite sum of numbers. However, they forget to prove first that this limes is finite (which you - purposely - skipped as well) before doing things with it which can only be made with finite values, In any case, you can prove that for their limes (expressing 0.9+0.09+0.009+...) while you will fail with 1+2+4+...

Ah, glad to see someone finally agrees with all my point of views on the subject :xmas10: !