I Broke Mathematics

[MarkFL]

$\begin{array}{rcl}a & = & b \\ a+a & = & a+b \\ 2a & = & a+b \\ 2a-2b & = & a+b-2b \\ 2(a-b) & = & a-b \\ 2 & = & 1 \end{array}$

Where did I go wrong?

 

[psalms 91]

lol I love it

 

[Lamb]

Ephesians 5:31

For this reason a man shall leave his father and mother and shall be joined to his wife, and the two shall become one flesh.

So 2 = 1 is correct

 

[ImaginaryDay2]

$\begin{array}{rcl}a & = & b \\ a+a & = & a+b \\ 2a & = & a+b \\ 2a-2b & = & a+b-2b \\ 2(a-b) & = & a-b \\ 2 & = & 1 \end{array}$

Where did I go wrong?

Care to explain your final step? There's no logic in it.

 

[Ruth]

Ephesians 5:31

For this reason a man shall leave his father and mother and shall be joined to his wife, and the two shall become one flesh.

So 2 = 1 is correct

How does that answer the op?

 

[MoreCoffee]

$\begin{array}{rcl}a & = & b \\ a+a & = & a+b \\ 2a & = & a+b \\ 2a-2b & = & a+b-2b \\ 2(a-b) & = & a-b \\ 2 & = & 1 \end{array}$

Where did I go wrong?

In the last step; 2*0 = 1*0 is correct but that does not mean 2 = 1

 

[MarkFL]

In the last step; 2*0 = 1*0 is correct but that does not mean 2 = 1

Yes, you correctly spotted the error...if $a=b$ then $a-b=0$ and in my last step I divided by zero (a mathematical no-no) to obtain the erroneous result.

Well done! :music:

 

[Lamb]

How does that answer the op?

I knew the answer was wrong but sometimes wrong answers aren't always what they appear to be. Hence the quote from scripture

 

[MoreCoffee]

Yes, you correctly spotted the error...if $a=b$ then $a-b=0$ and in my last step I divided by zero (a mathematical no-no) to obtain the erroneous result.

Well done! :music:

Not very well done; I have degrees in pure mathematics

 

[MarkFL]

Not very well done; I have degrees in pure mathematics

Well, that certainly gave you an advantage, but no one can fault you for using that here.

 

[MoreCoffee]

Well, that certainly gave you an advantage, but no one can fault you for using that here.

While at university, as an amusement for myself, I created a proof that 3 = 1 using a quadratic equation. How about you try the same, it is not so hard