NationStates Jolt Archive

I am probably wrong in these equations but here:

a=b
a*a=b^2
a*a+2=b^2+2
a*a+2(2)=b^2+2(2)
a*a+4=b^2+2(2) You can simp. one side without simp. the other
a*a+2=b^2(2)
a*a+1=b^2*1 or b^2
a^2+1=b^2
1=0


Like I said, I am probably wrong here so don't call me an idiot for not seeing something just point it out to me.

I am probably wrong in these equations but here:

a=b
a*a=b^2
a*a+2=b^2+2
a*a+2(2)=b^2+2(2)
a*a+4=b^2+2(2) You can sinp. one side without simp. the other
a*a+2=b^2*2
a*a+1=b^2*1 or b^2
a^2+1=b^2
1=0


Like I said, I am probably wrong here so don't call me an idiot for not seeing something just point it out to me.

how did you get from line 5 to 6? Did you leave the brackets out?

I think its correct.... :) :headbang: :sniper: :gundge:

its not.

a=b
a*a=b^2
a*a+2=b^2+2
a*a+2(2)=b^2+2(2)
a*a+4=b^2+2(2) You can sinp. one side without simp. the other
a*a+2=b^2*2
a*a+1=b^2*1 or b^2
a^2+1=b^2
1=0


Line six is incorrect.

Take line four (parentheses added for legibility):
(a*a)+2 * 2 = (b^2)+2 * 2 / 2
If you divide by two:
(a*a)+2 * 2 / 2 = (b^2)+2 * 2 /2
You're really multiplying by one (2/2 == 1), which gives us:
(a*a)+2 = (b^2)+2
Which is line three.

Problem right...

a*a+2(2)=b^2+2(2)
here-->a*a+4=b^2+2(2) You can sinp. one side without simp. the other
-->a*a+2=b^2*2

You divided a 2 out of the equation, but you also changed the sign from addition to multiplication.

It oughta be...

a*a + 4 = b^2 + 2(2)
a*a + 2 = b^2 + 2

Which still equals the same thing.

a=b
ok fine

a*a=b^2
fine

a*a+2=b^2+2
fine

a*a+2(2)=b^2+2(2)
fine

a*a+4=b^2+2(2) You can sinp. one side without simp. the other
fine (2*2=4)

a*a+2=b^2*2
I have a problem with this. Seems like you subtracted 2 from the left side, and then on the right side said that 2*2 = b^2 (because b^2*2 = b^2+b^2), which is not true. So you cant do that

a*a+1=b^2*1 or b^2
Here you subtracted one from the left side, and divided the right by 2, again, you cant do that.

a^2+1=b^2
1=0

a*a+4=b^2+2(2) You can sinp. one side without simp. the other
a*a+2=b^2*2
a*a+1=b^2*1 or b^2
a^2+1=b^2
1=0


From what I can see, there's a problem with how you got from the first line if this snippet to the second, and it's the same problem on down the line.

No because in the first side it was +2 and I had to divide by 2 so it was +1 while on the other side it was *2 and it would be *1. Sorry if that made no sense. Also I subtracted 2 from the four and two from the other side. I also may be wrong again.

It oughta be...

a*a + 4 = b^2 + 2(2)
a*a + 2 = b^2 + 2

Which still equals the same thing.

Actually:

a*a + 4 = b^2 + 2(2)
[a*a]/2 + 2 = [b^2]/2 + 2

But yeah, it still doesn't work.

No because in the first side it was +2 and I had to divide by 2 so it was +1 while on the other side it was *2 and it would be *1. Sorry if that made no sense. Also I subtracted 2 from the four and two from the other side. I also may be wrong again.

Nah its not that. How did you get from
a*a+4=b^2+2(2)
to
a*a+2=b^2(2)
?

I always knew logic had problems.

Actually:

a*a + 4 = b^2 + 2(2)
[a*a]/2 + 2 = [b^2]/2 + 2

But yeah, it still doesn't work.
it works if a=b=2.
But then the next line doesn't work.

You're not thinking about this one:
x^2-1=x^2-x, if x=1. Factorise each side
(x-1)(x+1)=x(x-1), simplify by (x-1)
x+1=x, substitute x=1
2=1

*blinks* all those obsecure values...

:( waaaahhh!! My head hurts!

Nah its not that. How did you get from
a*a+4=b^2+2(2)
to
a*a+2=b^2(2)
?

I subtracted the 2 right after the b^2 from the +4 and itself.

I subtracted the 2 right after the b^2 from the +4 and itself.
There's the problem!
On one side you did this:
a*a+4 -2 =a*a+ (+4-2) = a*a+2
That's fine.
However, you viewed the +2 on the second side as a seperate entity. It's not.
You tried doing this:
b^2+2(2) -2 =b^2(2) +2-2=b^2(2)
But unfortunately you can't do this. Because +2(2)-2 doesn't wipe out the +2, so you can slide the (2) over. It just takes a '2' away from this expression. You'll still be left with a 2. 2(2) means 2*2, which is equivalent to 2+2.
so:
b^2+2(2) - 2 = b^2+ (+2*2-2) = b^2+2

Sorry it's looking a bit complicated but I hope you understand. Easy enough mistake to make BTW

[You're not thinking about this one:
x^2-1=x^2-x, if x=1. Factorise each side
(x-1)(x+1)=x(x-1), simplify by (x-1)
x+1=x, substitute x=1
2=1[/QUOTE]


Your line, "simplify by (x-1)" is the same thing as dividing by 0, since you started by saying x=1. Since you can't divide by 0 and get a meaningful answer, the proof is wrong.

a=b
*Right.
a*a=b^2
*Right.
a*a+2=b^2+2
*Right.
a*a+2(2)=b^2+2(2)

*Ummm... No. Well, technically, yes the two sides are still equal... but only because of a coincidence (having a two on both sides already). If it had been, say a^2+2=b^2+3, then you could not multiply the second term of each side by the same number. In other words, you're missing a step:
a^2+2=b^2+2
a^2+2+2=b^2+2+2
a^2+4=b^2+4
But then I don't know why you wouldn't have just added 4 to each side in the first place. Unless you meant to use parentheses? (a^2+2)*2=(b^2+2)*2 ??

Let's see...

a*a+4=b^2+2(2)
a*a+2=b^2(2)

Ok. NO IDEA how you think you can do this. First, you subtract 2 from the left, so you would have to do so on the right as well... which would get you back to a^2+2=b^2+2. Of course, perhaps you DID mean parentheses before, in which case if you had simplified the left side and not the right you would have had:
2a^2+4=2(b^2+2)
And the only way to get the left side in this equation to match the one you have above is to divide by 2, which still gets you back to this:
a^2+2=b^2+2

Now, although it looks like you can't even get this far, you make other mistakes... and I wouldn't be helping you to ignore them. So, supposing we can get to a^2+2=2b^2, you have us do the following:

a*a+2=b^2(2)
a*a+1=b^2*1 or b^2

It looks like you want us to divide by 2 on both sides. But that gives you:
(a^2+2)/2=b^2(2)/2
(1/2)a^2+1=b^2

So, we've messed up again. Remember, if you divide or multiply in algebra, you have to perform the operation on every term in the expression.


Like I said, I am probably wrong here so don't call me an idiot for not seeing something just point it out to me.

Hey, everybody makes mistakes... But, you are not probably wrong... In the future, when something gives you a contradiction like 1=0, then realize that you have just told yourself that you either did something wrong, or assumed something incorrect. If you start thinking that you can validly "prove" things like 0=1, then you've abandoned the very basis of validity in mathematics.

I always knew logic had problems.

Sorry, but it doesn't. The proof is wrong.

Your line, "simplify by (x-1)" is the same thing as dividing by 0, since you started by saying x=1. Since you can't divide by 0 and get a meaningful answer, the proof is wrong.
I know, but it's a good way of showing to ppl what you're really doing when you say 'simplify'. Most ppl get it in their heads it means 'take away', not 'divide by'.

Line 6 is definately incorrect.

Well, now I see were I was wrong. Thanks for not bashing me like some others probably would.

This one works a little bit better, though it proves two equals one instead of one equals zero...

a = b (Opening statement)
a² = ab (Multiply each side by A)
a² - b² = ab - b² (Subtract B²)
(a - b) (a + b) = b (a - b) (Factoring each side)
(a + b) = b (Divide by a - b)
a + a = a (Subsitiution)
2a = a (Addition)
2 = 1 (Divide by A)

The operations are valid, though it still goes wrong in step five where I divided by (a - b). Since A and B are the same, it's dividing by zero.

I am probably wrong in these equations but here:

a=b
a*a=b^2
a*a+2=b^2+2
a*a+2(2)=b^2+2(2)
a*a+4=b^2+2(2) You can simp. one side without simp. the other
a*a+2=b^2(2)
a*a+1=b^2*1 or b^2
a^2+1=b^2
1=0


Like I said, I am probably wrong here so don't call me an idiot for not seeing something just point it out to me.

a=b
aa=b²
aa+2=b²+2
aa+2(2)=b²+2(2)
aa+4=b²+2(2)
aa+2=b²+2
...

That's where you're wrong ;), forget all the jargon all these lot are going into

basically, you tried to make + 2= x 2, which is illogical and impractical


Moreover, both a and b = 0 in your equation anyway, and so proves little of any substance.

a few mistakes, which im too lazy to point out or even identify properly. lets just say that, unless the foundation of all logic is erouneous ( unlikely and disastrous ) 1 shall never equal 0

a few mistakes, which im too lazy to point out or even identify properly. lets just say that, unless the foundation of all logic is erouneous ( unlikely and disastrous ) 1 shall never equal 0

Except in the case of very small values of 1 or very very large values of 0. ;)

I always knew logic had problems.

This ain't logic: this is set theory (and faulty set theory at that).

it works if a=b=2.
But then the next line doesn't work.

You're not thinking about this one:
x^2-1=x^2-x, if x=1. Factorise each side
(x-1)(x+1)=x(x-1), simplify by (x-1)
x+1=x, substitute x=1
2=1

Can't divide by x-1 if x=1 of course.
:)

Im seeing line 6 as incorrect, and i dont have the patience to read all the stuff could somone just explain to me why it is correct?

Im seeing line 6 as incorrect, and i dont have the patience to read all the stuff could somone just explain to me why it is correct?

5. a*a+4=b^2+2(2) You can simp. one side without simp. the other
6. a*a+2=b^2(2)

it appears to me that between lines 5 & 6 the original poster has subtracted 2 from both sides and then for some unknown reason has decided to multiply what remains on one side by 2. Labelling the operations for each step would have made a lot of sense, as would carrying out an initial substitution in line 2.

a=b
aa=ab multiply both sides by a
aa+2=ab+2 add 2 to each side
(aa+2)(2)=(ab+2)(2) multiply both sides by 2

what I get as a result of that is this: 2aa+4=2ab+4

whereas the original poster gets this: a*a+4=b^2+2(2)

Looks to me like they forgot to multiply a*a by 2, and the lack of brackets only serves to confuse everything, a trick that they will exploit later.

a=b
a*a=b^2
a*a+2=b^2+2
a*a+2(2)=b^2+2(2)
Shouldn' this look like 2([a^2]+2)=2(+2)? I didn't know you could multiply only part of a side of an equation. Of course, 2+2=4, so you could say you are adding 2 to both sides, but that's the same as adding 4 a line above. This step here just doesn't make sense to me.
[b]a*a+4=b^2+2(2) You can simp. one side without simp. the other
a*a+2=b^2(2)
How do you go from b^2+2(2) to b^2(2)? It would really help if you explained what exactly you did between these two steps.
a*a+1=b^2*1 or b^2
a^2+1=b^2
1=0
Yea...I'm just not seeing any sense in this equation...

No! Not fine! I'm not sure if this has been said before, but...you can't do that! If you want to multiply two to one side, you have to do it to the entire side, not just one element.
Yea, I'm not sure if anyone said it before me, but look up one post.

Oh, and after you answer the questions I point out at the post at the top of this page, also prove to me that 1 = 0 can be changed into a = a. The equation, to be a real proof, needs to be able to go both ways.