when 2 = 3

When I was young, I used to love Algebra 🙂 I remember taking el mo3asser exercise book, put some music on, make myself a hot cup of tea with milk and start solving problems for hours! It didn’t feel like studying at all! It was more of a game to me 🙂 

That’s why I was happy to find this on wikihow. It shows u how to prove that 2 can equal 3 after some logical algebra (and how u can prove it’s wrong). I heard about this simple game from my friends who studied engineering, but they forgot how to do it. So here it is: 

Let’s assume A = B

So 2 A = 2 B ;

and 3 A = 3 B ,


 Let’s multiply on both sides, the first equation with A and the second equation with B:

2 A2 = 2 A B

And 3 A B = 3 B2


Now we’ll subtract the second equation from the first one, so it will be:

2 A2 – 3 A B = 2 A B – 3 B2

Then we shift the 2’s on one side and the 3’s on the other side:

2 A2 – 2 A B = 3 A B – 3 B2

And we take common factors:

2 A (A – B) = 3 B (A – B)

Then we divide both sides with (A – B):

2 A = 3 B

And we assumed from the beginning that A = B, then:

2 A = 3 A


Which means that 2 = 3 J

 (Bas 3ala fekra, there is a minor trick in the logical solution that proves that 2 can never equal 3.) 


4 responses to “when 2 = 3

  1. Simple, since A = B, then A – B = 0. Therefore 2A(A-B) = 3B(A-B) = 0 which perfectly makes sense. Dividing both sides by A – B also means division by zero, which results in both sides being equal to infinity which is also a valid solution!

  2. Cute 🙂 reminds me of the one about the 3 people who go to buy a stereo, the store owner is out, boy tells them it costs 30 LE. Each guy pays 10. Storeowner returns, repremands the boy for charging them that much, tells him it’s only 25 LE and gives him 5 LE to return. Boy is greedy, he pockets 2 LE, chases the guys and gives each 1 LE back. Now each guy paid how much? 10-1=9. So between the three of them they paid 3*9=27. If we add the 2 LE in the boy’s pocket you end up with 29 LE. Where did the last pound go?? 😀

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