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  1. We can find the first false inference by finding the first $\rm\color{#c00}{false\ equation}$ above; if it is equation number $\rm\: n\!+\!1,\:$ then the inference from equation $\rm\:n\:$ to $\rm\:n\!+\!1\:$ must be incorrect.

  2. Error. Usually, if a proof proves a statement that is clearly false, the proof has probably divided by zero in some way. In this case, the quantity of is as , since one cannot divide by zero, the proof is incorrect from that point on. Thus, this proof is false.

  3. 29 Ιουλ 2010 · The equality $nx = x^2$ is not comparable to an equality like $\sin x^2 = 1 - \cos x^2$ : the equation $nx = x^2$ holds for only two values of $x$, where as the trigonometric equation holds for any real/complex value of $x$.

  4. 23 Οκτ 2015 · I need to find the flaw in the following proof: $a,b\in\mathbb{R}$\ $\left\{ 0 \right\} $ such that $a=b$ 1) Multiplying both sides by $a$ yields the equality: $a^2=ab$ 2) Subtracting $b^2$ from...

  5. 1=2: A Proof using Beginning Algebra. The Fallacious Proof: Step 1: Let a = b . Step 2: Then , Step 3: , Step 4: , Step 5: , Step 6: and . Step 7: This can be written as , Step 8: and cancelling the from both sides gives 1=2. See if you can figure out in which step the fallacy lies.

  6. 12 Ιουλ 2022 · Some people think that 1=2, and the math actually makes sense. But can you prove them wrong and find the flaw in their logic?

  7. From x^2 = x, you get x = 1. If you take ln x and x = 1, then ln x = ln 1 = 0. When you have 2 ln x = ln x, you have 2 * 0 = 0. Then you tried to divide both sides by 0 which is not possible. When you divide by zero, you get an indeterminant result, so any proof that requires you to divide by zero cannot be trusted to give you any meaningful ...

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