# Thread: Math proof. Find the error.

1. ## Math proof. Find the error.

Ok, so I like math. I found this simple proof when I was in college and thought it was nifty. But, there is an error in it that nullifies it's argument. Can you find it?

a = b

a^2 = a*b

a^2 - b^2 = a*b - b^2

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

(a + b) = b

b + b = b

2b = b

2 = 1

If you have any other fun math problems or proofs list them! I realize that this probably isn't going to be a popular subject, but as a math geek I was hoping that perhaps others might think it is interesting.

2. Originally Posted by Alavatar
a = b
<snip out the worthless steps>
(a + b)*(a - b) = b*(a - b)
(a + b) = b
If a=b, then a - b = 0

Can't divide by 0

3. Step 1: -1/1 = 1/-1

Step 2: Taking the square root of both sides:

Step 3: Simplifying:

Step 4: In other words, i/1 = 1/i.

Step 5: Therefore, i / 2 = 1 / (2i),

Step 6: i/2 + 3/(2i) = 1/(2i) + 3/(2i),

Step 7: i (i/2 + 3/(2i) ) = i ( 1/(2i) + 3/(2i) ),

Step 8: ,

Step 9: (-1)/2 + 3/2 = 1/2 + 3/2,

Step 10: and this shows that 1=2.

Roll with the complex number fun.

4. grumbles. I hate math. Pick a different subject LOL.

5. Originally Posted by Darkschneider
Step 1: -1/1 = 1/-1

Step 2: Taking the square root of both sides:

Step 3: Simplifying:

Step 4: In other words, i/1 = 1/i.

Step 5: Therefore, i / 2 = 1 / (2i),

Step 6: i/2 + 3/(2i) = 1/(2i) + 3/(2i),

Step 7: i (i/2 + 3/(2i) ) = i ( 1/(2i) + 3/(2i) ),

Step 8: ,

Step 9: (-1)/2 + 3/2 = 1/2 + 3/2,

Step 10: and this shows that 1=2.

Roll with the complex number fun.
Wow this one racked my brain a bit!

I think the fault is in the proof for i/1 = 1/i?

sqrt(1/-1) = sqrt(-1/1) -> i = i

I am not completely positive, just confused. Because if you multiply (1/i)*(i/i) you get (-i), which is not i/1. Or perhaps complex numbers just throw a wrench in basic algebra?

6. Originally Posted by Darkschneider
If a=b, then a - b = 0

Can't divide by 0
Oh, and correct.

Also, a^2 - b^2 = a*b - b^2 is 0 = 0. Factor 0 and you still are at 0. Divide 0/0 and you get infinity.

Simple algebra, but it's fun.

Hairy math = advanced electrical engineering stuff. Whoa, that stuff is beastly.

7. Originally Posted by Alavatar
Whoa, that stuff is beastly.
But fun, if only I'd gotten here sooner...got anything else?

8. Originally Posted by DKerrigan
But fun, if only I'd gotten here sooner...got anything else?
I don't. The one I posted is the only trick proof I have and I was hoping others might have stuff.

9. I feel..........not smart.

10. Originally Posted by Alavatar
Ok, so I like math. I found this simple proof when I was in college and thought it was nifty. But, there is an error in it that nullifies it's argument. Can you find it?

a = b

a^2 = a*b

a^2 - b^2 = a*b - b^2

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

(a + b) = b

b + b = b

2b = b

2 = 1

If you have any other fun math problems or proofs list them! I realize that this probably isn't going to be a popular subject, but as a math geek I was hoping that perhaps others might think it is interesting.
Well I saw the accepted answer and I'm not really sure.

My thinking is this.

If (a + b) = b then a and b must be zero.

If b+b=b then a and b must be zero.

If 2b=b then a and b must be zero.

2 can not equal 1

Trying to solve a proof that can not possibly be correct will obviously lead to impossible operations.

a = b

a^2 = a*b

a^2 - b^2 = a*b - b^2

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

0=0

11. Originally Posted by joker965

<SNIP>
Kind of. The problem with the proof is in the 3rd step.

If a = b then a^2 - b^2 = 0 and ab - b^2 = 0, so anything after that is just manipulating the number 0.

12. Originally Posted by Alavatar

a = b

a^2 = a*b

a^2 - b^2 = a*b - b^2
if a=b then a^2=b^2 subtracting made left side =0
if a=b then a*b=b^2 subtracting them made right side =0
you made both sides =0...which is true...but sad.
(a + b)*(a - b) = b*(a - b)
a=b so subtracting a-b and multiplying through made left side =0 still ok...
a=b so subtracting a-b and multiplying through made right side =0 ok..ok...
(a + b) = b
since a-b=0...you divided both sides by zero...you! you! you! You cant do that....
you cant divide anything by zero and get any real answer...you are mean....I hate you!
b + b = b
BLllllTTTTttT
2b = b
wrong!
2 = 1
WrOngE SuX0R
i hate this...

13. Here is a practice question I came up with about 2 years ago (I had to resolve it to remember how to do it. ). I originally made it for my co-workers, none of them answered it except to say they had more important work to do!

An airplane is cruising at an altitude of 2500ft and velocity of 500 ft/s. The airplane begins ascending along the parabolic path y = 0.0005x^2 + 2500 while it's air-speed indicator maintains the velocity of 500 ft/s. After traveling 1500 horizontal (x = 1500) feet the airplane releases it's cargo so now the cargo is in freefall. Assume no air resistance.

A) If y=0 and the ground is assumed to be completely flat where does the cargo land?
B) How long was the cargo in freefall?
C) What is it's impact velocity in ft/s?
D) What angle (in degrees) was the cargo released?
E) What angle did the cargo impact the ground?

14. Originally Posted by Alavatar
Here is a practice question I came up with about 2 years ago (I had to resolve it to remember how to do it. ). I originally made it for my co-workers, none of them answered it except to say they had more important work to do!

Hmm, Just a question. If air resistance = 0 wouldn't flight be impossible?

15. Originally Posted by Vardak
Hmm, Just a question. If air resistance = 0 wouldn't flight be impossible?
Technically, yes. But this is a math problem designed to facilitate the use of basic physics equations. Air resistance is considered a bit more advanced then 'basic' physics. Besides, I just didn't want to deal with ODEs.

Edit: Also, with air resistance you need to specify a whole bunch of new data such as shape of the cargo, mass, rotation of the object in freefall (unless cargo is spherical), etc. A big PITA that I haven't had to deal with for about 5 years, now, and I don't really want to search through my books to relearn this right now.

16. I'm going to the dragonlance movie website and wash this math stuff from my brain.

17. i didnt understand the responses that came after but this is what i thought when i first read it

a = b/////a=a correct

a^2 = a*b/////2a = 2a correct

a^2 - b^2 = a*b - b^2/////2a - 2a = 0/////2a - 2a = 0 correct

(a + b)*(a - b) = b*(a - b)///// 2a * 0 = 0/////a * 0 = 0

(a + b) = b///// 2a = a not correct

b + b = b///// not correct for the same reason

2b = b///// not correct for the same reason

2 = 1 im confused i dont think i know how proofs work i guess it doesnt help that ive been up all night

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