#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.

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.

#2

you factored wrong

edit: maybe you didn't. lemme check again...

EDIT2: yes, you did factor wrong

edit: maybe you didn't. lemme check again...

EDIT2: yes, you did factor wrong

#3

2=/=1 because two is not one!!! theres a mistake in your equation

#4

no your doing it wrong

#5

you factored wrong

edit: maybe you didn't. lemme check again...

EDIT2: yes, you did factor wrong

How so?

#6

You divided by 0. /thread

#7

there is a fallacy...no one cares.... (look at me, I can do math proofs).....

#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

x = .999...

10x = 9.999...

10x - x = 9.999... - .999...

9x = 9

x = 1

since x=x

therefore .999... = 1

#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.

#10

Well isn't this pointless.

#11

is a^2 the same as 2a? is that the problem?

#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?

therefore the proof falls apart after that.

and 0.9999 recurring = 1.

k?

*Last edited by Sol9989 at May 21, 2008,*

#13

He factored correctly, but a+b=b means that a=0

#14

never divide by 0!!!!!!!!!!!!!!!!!!!!!! the penalties are immense.

#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...

#17

if a=b, a-b=0 so you can't divide by it.

and 0.9999 recurring = 1.

k?

Spoil the fun

#18

you touch yourself at night.

#19

Spoil the fun

that's what i'm here for.

#20

1. he divided with (a-b)=0

2..999x10 =9990...

2..999x10 =9990...

#21

If you wrote out the whole question perhaps we could find out instead of giving us the working out.

#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.

a=0 (Subtract b from each side)

a = b

0 = 0

You only decided to determine a = 1 without any proof.

#23

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

I am SO showing my geometry teacher that tomorrow.

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

0.999999...= 1/thread

*Last edited by real_québécois at May 21, 2008,*

#25

I am SO showing my geometry teacher that tomorrow.

s/he probably knows it's true already.

#26

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

#27

Wait... 10(.999) is 9.99, not 9.999

Dangit!

Dangit!

#28

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

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.

#30

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

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

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...

#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.

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.

#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

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

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

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.

#35

yay! math discussions!

#36

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..

They are infinite....

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..

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

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.

#39

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

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.

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.