#Experiment#Proof#mathematics
Did you know that 1 = 2 ?
How to proof 1 = 2
How to Prove That 1 = 2
Let's begin our journey into the bizarre world of apparently correct, yet obviously absurd, mathematical proofs by convincing ourselves that 1 + 1 = 1. And therefore that 2 = 1. I know this sounds crazy, but if you follow the logic (and don't already know the trick), I think you'll find that the "proof" is pretty convincing.
Here's how it works:
Assume that we have two variables a and b, and that: a = b
Multiply both sides by a to get: a2 = ab
Subtract b2 from both sides to get: a2 - b2 = ab - b2
This is the tricky part: Factor the left side (using FOIL from algebra) to get (a + b)(a - b) and factor out b from the right side to get b(a - b). If you're not sure how FOIL or factoring works, don't worry-you can check that this all works by multiplying everything out to see that it matches. The end result is that our equation has become: (a + b)(a - b) = b(a - b)
Since (a - b) appears on both sides, we can cancel it to get: a + b = b
Since a = b (that's the assumption we started with), we can substitute b in for a to get: b + b = b
Combining the two terms on the left gives us: 2b = b
Since b appears on both sides, we can divide through by b to get: 2 = 1
Wait, what?! Everything we did there looked totally reasonable. How in the world did we end up proving that 2 = 1?
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