Questions tagged [fake-proofs]

Seemingly flawless arguments are often presented to prove obvious fallacies (such as 0=1). This is the appropriate tag to use when asking "Where is the proof wrong?" about proofs of such obvious fallacies.

An example of a fake proof is $$1=\sqrt{-1\cdot-1}=\sqrt{-1}\sqrt{-1}=i^2=-1$$ which fails because $\sqrt{xy}=\sqrt x\sqrt y$ does not hold if $x$ or $y$ is negative. Sometimes the proof may be presented as a puzzle, the challenge being to identify the flaw.

For asking about identifying flaws in general proofs ("spot the mistake"); the tag should instead be used.

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Goldbach's Theorem

Is this a proof for Goldbach's Theorem? I'm assuming not, but where does it go wrong? The theorem states that any even number greater than 2 can be represented as the sum of two numbers. Let $p_1$ and $p_2$ be two prime numbers. $n = p_1 + p_2;…
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Bogus prove of the irrationality of $\sqrt{\frac{1}{2}}$.

I need help figuring out my mistake. Proof. Proving by contradiction that $\sqrt{\frac{1}{2}}$ is irrational. Suppose $\sqrt{\frac{1}{2}}$ is rational so: $\sqrt{\frac{1}{2}}=\frac{m}{n}$. Where $m/n$ are in lowest terms. Squaring both sides and…
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