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.
1,331 questions
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Are n-vectors linear functionals of n-forms? Or of (n-1)-forms?
Summary of question: Are tangent vectors $ v \in T_p M$ linear functionals of $0$-forms on $M$, or of 1-forms on M?
Likewise are $n$-blades $v_1 \land \dots \land v_n \in \Lambda^n( T_p M)$ (and more ...
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Where is the fact that $\Omega \ne \mathbb C$ really used in the Riemann Mapping Theorem?
I am struggling to understand where the assumption $\Omega \ne \mathbb C$ is used in the proof of the Riemann Mapping Theorem in "Real and Complex Analysis" by Rudin. It looks to me that he ...
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Irrationality of Euler's constant: where is my proof wrong? [closed]
I've had another look into Euler's constant since my last post and developed the argument below. I'm new to number theory, so am wondering where this might go astray? Can someone point out the error ...
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Why can the flat torus be isometrically embedded in the 3-sphere $\mathbb{S}$^3?
Question: Why is it possible to isometrically embed the flat torus inside of the 3-sphere? (Clifford torus) Even though the flat torus has zero Gaussian and mean curvature, whereas the 3-sphere has ...
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does $1^0 = 1^1$ imply $0 = 1$? (Without using logarithms)
I understand that:
$\text{$1^0 = 1$ and $1^1 = 1$}$
so it follows that:
$1^0 = 1^1.$
However, I’ve come across the mistaken reasoning that this might imply $0 = 1$, based on the idea that if $ a^...
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Product to sum rule for the formal power series of the Logarithm seems to lead to a contradiction
According to
Ivan Niven. Formal Power Series. The American Mathematical Monthly, 76 (8), (1969), 871-889.
for the formal logarithm, defined as
$$
\log(1+B)=\sum_{k=1}^\infty\frac{(-1)^{k+1}}{k}B^k
$$...
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A "proof" that any matrix with a left inverse is a bijection [duplicate]
What's the flaw in this "proof"?
Claim: If matrix $A$ has a left inverse, then $A$ is a bijection.
"Proof": We will show that $A$ is an injection and also a surjection, and ...
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Eigenvalues of a complex orthogonal matrix
Property 1:A complex orthogonal matrix must have eigenvalues with modulus 1.
Property 2: If all entries in the matrix are real (real orthogonal matrix), then the eigenvalues must be $\pm 1$
Proof of ...
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Is it possible to substitute 'definable' for 'recursive' in Gödel's first incompleteness theorem?
I'm reading Godel incompleteness theorem from "A mathematical introduction to logic" by Enderton.
GÖDEL INCOMPLETENESS THEOREM (1931)
If $A$ ⊆ Th $\mathbb{N}$ and $\#A$ is recursive, then Cn ...
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Incorrect use of complex sine causes $\sin\frac {4\pi}{9}$ to evaluate to $0$ [closed]
I would like to know where I have gone wrong here (apologies for any inconsistent notation)
$$\begin{align}
\sin\left(\frac {4\pi}{9}\right)
&= \frac{1}{2i}\left(
e^{ i\,\frac{4\pi}{9}}
- e^{-...
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What is wrong with this proof showing that every solution of the boundary problem has infinitely many zeroes on (0,1)?
I had an assignment in which one question was :
Prove that any solution $y:(0,1) \rightarrow \mathbb{R}$ of the boundary value problem $$y'' + \frac{4\pi^2}{1-x^2}y = 0$$ has infinitely many zeroes.
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What is the flaw in this false proof that the set of limit points for a union of sets is equal to the union of sets of limit points of said sets?
Does anybody know the flaw in this false proof stating that the set of limit points for a union of sets is equal to the union of sets of limit points of said sets? Thank you!
Let $\left(X,\mathcal{T}\...
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Order of the Koch Curve
This question goes beyond any math I've formally studied, so apologies if I explain it poorly.
For whatever reason I was imagining trying to create a function that would input real numbers and output ...
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Let $q \in \mathbb{N}$ .Prove that if $q+2$ is a prime then $q2^q +1$ is not a prime
I would like to know what is wrong with the proof I came up with:
Let $q \in \mathbb{N}$
Since $q+2 \equiv 0$ (mod $q+2$), we get $q \equiv -2$
Therefore $q2^q +1 \equiv -2*2^q +1 \equiv -2^{q+1} +1$ ...
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What is wrong with this proof by induction that $n = O(1)$? [closed]
The proof uses the sum rule for big-O: $O\{f(n)\} + O\{(g(n)\} = O\{\text{max}[f(n),g(n)]\}$, which reads "The sum of a function that is big-O of $f(n)$ and a function that is big-O of $g(n)$ is $...
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