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#1
2 = 1?

Look.

a=b

a^2=ab <---Multiply both sides by a

a^2-b^2=ab-b^2 <--- subtract both sides by b^2

(a+b)(a-b)=b(a-b) <---Factor

(a+b)(a-b)/a-b=b(a-b)/a-b <---Divide both sides by a-b

cancel the a-b's

Therefore you end up with...

a+b=b

Now if a=1 you get 2=1

There is a fallacy, find it.
Quote by Meths

Obviously I'm biased towards the correct point of view. What kind of retard isn't?


#2
you factored wrong
edit: maybe you didn't. lemme check again...
EDIT2: yes, you did factor wrong
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#5
Quote by nexteyenate
you factored wrong
edit: maybe you didn't. lemme check again...
EDIT2: yes, you did factor wrong

How so?
Quote by Meths

Obviously I'm biased towards the correct point of view. What kind of retard isn't?


#8
Try this one; I can prove that .999... = 1.0

x = .999...
10x = 9.999...
10x - x = 9.999... - .999...
9x = 9
x = 1
since x=x
therefore .999... = 1
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#9
There is a way some people end with 1=2 but the fact is that they have to divide by 0 at some point of the problem, which can lead to John Petrucci killing you by shredding next to you.
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#10
Well isn't this pointless.
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#12
if a=b, a-b=0 so you can't divide by it.

therefore the proof falls apart after that.

and 0.9999 recurring = 1.

k?
"And after all of this, I am amazed...

...that I am cursed far more than I am praised."
Last edited by Sol9989 at May 21, 2008,
#14
never divide by 0!!!!!!!!!!!!!!!!!!!!!! the penalties are immense.
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#15
We got this problem as extra credit back in Algebra 2, unfortunately I wasn't paying attention when they went through it but it is something with what Sol9989 is saying...
#16
I posted an almost similar thread... dunno, check the divizion by zero thing...
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#17
Quote by Sol9989
if a=b, a-b=0 so you can't divide by it.

and 0.9999 recurring = 1.

k?

Spoil the fun
Quote by Meths

Obviously I'm biased towards the correct point of view. What kind of retard isn't?


#19
Quote by preludetowar
Spoil the fun


that's what i'm here for.
"And after all of this, I am amazed...

...that I am cursed far more than I am praised."
#20
1. he divided with (a-b)=0
2..999x10 =9990...
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#21
If you wrote out the whole question perhaps we could find out instead of giving us the working out.
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#22
a+b=b
a=0 (Subtract b from each side)
a = b
0 = 0
You only decided to determine a = 1 without any proof.
#23
Quote by Riddler
Try this one; I can prove that .999... = 1.0

x = .999...
10x = 9.999...
10x - x = 9.999... - .999...
9x = 9
x = 1
since x=x
therefore .999... = 1


I am SO showing my geometry teacher that tomorrow.
#24
Quote by Msu_Man04
I am SO showing my geometry teacher that tomorrow.


This will result in your teacher making fun of your ignorance.

0.999999...= 1/thread
Brokeback Lego - Animation Movie I Made

Quote by \GuitarHero/
Our band mascot is a Muffin.



A recent study shows that 8% of teenagers listen to nothing but music with guitars in it. Put this in your sig if you're one of the 92% who aren't close-minded morons.
Last edited by real_québécois at May 21, 2008,
#25
Quote by Msu_Man04
I am SO showing my geometry teacher that tomorrow.


s/he probably knows it's true already.
"And after all of this, I am amazed...

...that I am cursed far more than I am praised."
#26
Quote by Riddler
Try this one; I can prove that .999... = 1.0

1. x = .999
2. 10x = 9.990
3. 10x - x = 9.990 - .999
4. 9x = 8.991
5. x = .999
since x=x
therefore .999... = .999


that equation was lame, and if you didnt spot that you are an idiot. i numbered the steps as i was working it for a second to help me incase i made any errors
#28
Quote by Sol9989
s/he probably knows it's true already.

I showed a few of my math teachers that mathematical paradox, only one knew it.

(although I do it differently)

(1/3) = .333...

.333... * 3 = .999...
(1/3) * 3 = 1
#29
Quote by lordofthefood1
I showed a few of my math teachers that mathematical paradox, only one knew it.

(although I do it differently)

(1/3) = .333...

.333... * 3 = .999...
(1/3) * 3 = 1



0,33333... x 3 = 1, not ,999999...

That's the whole point only a few person on the pit seem to understand.
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Quote by \GuitarHero/
Our band mascot is a Muffin.



A recent study shows that 8% of teenagers listen to nothing but music with guitars in it. Put this in your sig if you're one of the 92% who aren't close-minded morons.
#30
Quote by real_québécois
0,33333... x 3 = 1, not ,999999...

That's the whole point only a few person on the pit seem to understand.

Quote by lordofthefood1
I showed a few of my math teachers that mathematical paradox, only one knew it.


it's hardly a paradox.

http://en.wikipedia.org/wiki/0.999...
"And after all of this, I am amazed...

...that I am cursed far more than I am praised."
#31
a=b

a^2=ab

a^2-b^2=ab-b^2 <----these are the exact same

however, since b^2 = a^2, the first group equals 0
as well, since a=b, then a^2 = ab, and thus the 2nd group equals zero

from here, you're already finished.

but, if we continue

(a+b)(a-b)=b(a-b)

even now, it still equals zero, since a-b = a-a = 0

but continuing nevertheless

(a+b)(a-b)/(a-b)=b(a-b)/(a-b)

Here, you not only have zero as a numerator, but also as a denominator

Thus the correct answer is undefined.

As in a+b = b = undefined.
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#32
You're doing this wrong, pal

It's this way:

You started stating that a=b

So you've got (for example): a=4

a=b

a-b= 0

4-4= 0

You're disagreeing with yourself when saying that a=b, because at the end you fnish saying that a=2 and b=1
#33
Quote by real_québécois
0,33333... x 3 = 1, not ,999999...

That's the whole point only a few person on the pit seem to understand.


No, 3.3 cont. times 3 equals 9.9 cont. 3+3+3 never adds up to 10, no matter how many times you do it, so even if the decimal goes infinite places.... there are never enough 3s.
#34
Quote by Msu_Man04
No, 3.3 cont. times 3 equals 9.9 cont. 3+3+3 never adds up to 10, no matter how many times you do it, so even if the decimal goes infinite places.... there are never enough 3s.


How old are you? You're not doing math anymore...you're just playing randomly with numbers.
Brokeback Lego - Animation Movie I Made

Quote by \GuitarHero/
Our band mascot is a Muffin.



A recent study shows that 8% of teenagers listen to nothing but music with guitars in it. Put this in your sig if you're one of the 92% who aren't close-minded morons.
#36
Quote by real_québécois
How old are you? You're not doing math anymore...you're just playing randomly with numbers.


I'm 15, thank you. And I'm not just 'playing randomly with numbers'.

The only reason (technically) 3.333... goes on infinitely is in an attempt to get it closer to 1, correct? Well, no matter what, its 3.333 x 3. And three 3s always adds to 9. So... 3.3 x 3 is 9.9.... 3.33 x s is 9.99... et cetera. If 3.333.... x 3 eventually added to 1, there would be no point to have this debate in the first place.

Don't assume im some uneducated child (which you must have, since you asked for my age) because you don't understand what I'm implying.
#37
a-b=0?
Eh, division by zero? There is an axiom that tells you can't divide by zero?

Oh, and 0.999... =1, just as 1/3= 0.333333... etc..

Quote by Msu Man04
No, 3.3 cont. times 3 equals 9.9 cont. 3+3+3 never adds up to 10, no matter how many times you do it, so even if the decimal goes infinite places.... there are never enough 3s.


They are infinite....

Last edited by gonzaw at May 21, 2008,
#38
Quote by Msu_Man04
I'm 15, thank you. And I'm not just 'playing randomly with numbers'.

The only reason (technically) 3.333... goes on infinitely is in an attempt to get it closer to 1, correct? (???)Well, no matter what, its 3.333 x 3. And three 3s always adds to 9. So... 3.3 x 3 is 9.9.... 3.33 x s is 9.99... et cetera. If 3.333.... x 3 eventually added to 1, there would be no point to have this debate in the first place.

Don't assume im some uneducated child (which you must have, since you asked for my age) because you don't understand what I'm implying.


http://en.wikipedia.org/wiki/0.999...

k? shush now.
"And after all of this, I am amazed...

...that I am cursed far more than I am praised."
#39
Quote by Sol9989


I've read that already.

Just because .999... is 'generally accepted' to be 1, or whatever, doesn't mean it is. For all... say, measurement purposes and other uses, yes, it is close enough to be one. But literally it is not. That's why it's .999... and not 1.
#40
Quote by Msu_Man04
I've read that already.

Just because .999... is 'generally accepted' to be 1, or whatever, doesn't mean it is. For all... say, measurement purposes and other uses, yes, it is close enough to be one. But literally it is not. That's why it's .999... and not 1.


Quote by wikipedia
In mathematics, the recurring decimal 0.999… denotes a real number equal to 1. In other words, the notations "0.999…" and "1" represent the same real number.


they are the same. why is it so hard to grasp? it's like someone telling you 1+1=2 when you were 2 years old or whatever and then you throw a big hissy fit because you don't want to accept it.
"And after all of this, I am amazed...

...that I am cursed far more than I am praised."
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