Mathematicians explain where the error is.

[Bird222]

I saw this online and I don't see where the error is being made.

x=y
Rewrite as 2x-x=2y-y

1. add x to both sides and get. 2x=2y-y+x
2. add y to both sides and get 2x+y=2y+x
3. subtract 2y from both sides and get 2x+y-2y=x
4. subtract y from both sides and get 2x-2y=x-y
5. rewrite as 2(x-y)=x-y
6. divide both sides by x-y and get 2=1

I know this is obviously wrong but why? Is it because in essence you are dividing by 0 in step 6 and you can't divide by 0?

Why is this wrong?

 

[sandorski]

2x-x=x
2y-y=y
x=y

Too long since I have done this shit, so I know that doesn't work as the answer

 

[dasherHampton]

I'm not math genius. Ask me what my overall cost basis is if I have 1000 shares at 49, 2000 shares at 51, and 1500 shares at 53 and I'll respond with a blank stare.

But even I know you can't divide by zero. That fucks everything up.

I had a friend who WAS a math whiz and he used to amuse himself hiding divisions by zero in these sorts of problems to come up with all sorts of whacked solutions.

 

[DaveSimmons]

You start by assuming x=y so by definition x-y is x-x is 0. Yes, dividing by 0 in step 6 generates nonsense results.

It's like in formal logic where if you assume true = false, then you can "prove" anything that you want including 1=2.

 

[Chaotic42]

I saw this online and I don't see where the error is being made.

x=y
Rewrite as 2x-x=2y-y

1. add x to both sides and get. 2x=2y-y+x
2. add y to both sides and get 2x+y=2y+x
3. subtract 2y from both sides and get 2x+y-2y=x
4. subtract y from both sides and get 2x-2y=x-y
5. rewrite as 2(x-y)=x-y
6. divide both sides by x-y and get 2=1

I know this is obviously wrong but why? Is it because in essence you are dividing by 0 in step 6 and you can't divide by 0?

Why is this wrong?

x-y is by definition zero. Since you can't divide by zero, your error is in step 6.

 

[JEDIYoda]

damn another please do my homework for me thread?????

 

[Bird222]

damn another please do my homework for me thread?????

Definitely not. lol

 

[snoopy7548]

2x - x = 2y - y

Let x = y

x = y

I'm an engineer and I don't like math, but that makes sense and works.

 

[JTsyo]

2=1

Well that's true, 2=1 for large values of 1.

 

[dank69]

nvm

 

[Perknose]

You start by assuming x=y so by definition x-y is x-x is 0. Yes, dividing by 0 in step 6 generates nonsense results.

It's like in formal logic where if you assume true = false, then you can "prove" anything that you want including 1=2.

^^^ This.

 

[rh71]

First tell me how this applies to real life.

/don't let my kids hear that.

 

[dullard]

Start by removing anything that is there just to confuse. If x equals y, then it can also be set to equal a third symbol, z. First, I'll just substitute z in everywhere to remove much of the confusion.

Remove one layer of obfuscation:
x = y = z
Rewrite as 2 * z - z = 2 * z - z (this is clearly true, but is just a distraction)

1: 2 * z = 2 * z - z + z (This is clearly true, but is just a distraction)
2: 2 * z + z = 2 * z + z (This is clearly true, but is just a distraction)
3: 2 * z + z - 2 * z = z (This is clearly true, but is just a distraction)
4: 2 * z - 2 * z = z - z (This is clearly true, but is just a distraction)
5: 2 * (z - z) = (z - z) (This is clearly true, but it is just saying 0 = 0)

So, basically all steps up to #5 are distractions and are unnecessary. Lets just restart at #5 where the problem really should have started without fluff:

Problem without fluff:

5: 2 * (0) = (0) (Yes, 2 times zero is zero)
6: Divide both sides by 0 and get 2 * (0 / 0) = (0 / 0)

The issue is that 0 / 0 is undefined. I wouldn't call it wrong to divide by zero, but you have to know that the result is not likely to be of any use. So, lets just call the undefined answer to 0 / 0 as "something". Then you get the final answer:

Final Answer:

7: 2 * (something #1) = 1 * (something #2)
8: 2 = 1 * (something #2 / something #1)

That final line is correct, although it is useless information.