# 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.

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### $\int_0^x g(x-a)f(a)da=\int_0^x f(a)da$ - Please help to explain the error

Let $I$ be an integral function s.t. $$I(f(x))= \int_0^x f(a)\,da.$$ Let $g$ be a function s.t. $g(0)=1$ and $g_x(a):=g(x-a)$. I have \begin{align} \int_0^x g_x(a)f(a)\,da& =I(g_x(x)f(x)) \\[...
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### different answers for same division

I recently came across an easy question which stumped me . It is as follows: simplify the following expression a/b/c/d/e/f . My approach: for a/b/c/d it's easy to see as dividing a fraction (a/b) ...
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### Prove that $\; U\setminus A = U \iff A=\emptyset\;$ where $U$ is the universe (False proof of the opposite).

I think I might have made a false proof for the following problem but I can´t seem to find where the flaw is. Prove that $\displaystyle \; U\setminus A = U \iff A=\emptyset\;$ where $U$ is the ...
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### Why is it so difficult to prove the irrationality of the zeta function for $N$?

I know that no one has yet been able to prove that the zeta function is irrational at every point $N$. but my question is why is it so difficult to prove the irrationality of the zeta function for $N$?...
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### Understanding where my naive attempt to prove Countable Choice out of Finite Choice fails

I am aware of this and this topic, but I would like to receive a clarification concerning the foregoing naive attempt to prove Countable Choice, to see if I understood properly the question. Assume ...
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### Why is P(A⋃B) ⊄ P(A)⋃P(B)?

I had a question in my 11th grade Mathematics book : Prove that P(A⋃B) ⊄ P(A)⋃P(B) I did a proof for why P(A⋃B) ⊂ P(A)⋃P(B) Which step in the following proof is wrong? ...
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### Is $\sin(\alpha)=\frac{\tan(\alpha)}{\sqrt{1+\tan^2(\alpha)}}$ a true statment?

I'm being asked to prove the following equality $$\sin(\alpha)=\frac{\tan(\alpha)}{\sqrt{1+\tan^2(\alpha)}}$$ and I support the idea that they are not equal (the rest of my class seems to desagree ...
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### Resolving a gap in the Kernel proof of the Dirichlet Integral

One well known proof of the Dirichlet Integral is to use the kernel $\frac{\sin{(2n+1)x}}{\sin{x}}$ and applying the Riemann-Lebesgue Lemma to an auxiliary function to obtain an equivalence between ...
Suppose someone does research on a phenomenon and builds the model $y=a+bx$. The scientist then states the "Theorem" that, given the particular assumptions leading to the model, $x$ affects $y$ ...