Math proof. Find the error.

[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.

[Darkschneider]

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

[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.

[Cupcake]

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

[Alavatar]

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?

[Alavatar]

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.

[DKerrigan]

Whoa, that stuff is beastly.

But fun, if only I'd gotten here sooner...got anything else?

[Alavatar]

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.

[ehondajim]

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

[joker965]

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

[Alavatar]

<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.

[Yvonne_Blacksword]

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...

[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!

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?

[Vardak]

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?

[Alavatar]

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.

[Tous]

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

[Reisei]

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