# 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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### Is the category of measurable spaces MONOIDAL closed? (fake-proof)

As discussed on MathOverflow, there is a preprint on ArXiv that claims the category of measurable spaces is monoidal closed (in particular that exponential objects $Y^X$ always exist and have ...
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### Fake Proof for Dimension of $SO(n)$ (rotations)?

Because there are $\binom{n}{2}$ distinct planes spanned by the elements of any given orthonormal basis for $\mathbb{R}^n$, it seems to follow readily (because apparently planar rotations generate all ...
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### Why is this proof wrong? $2^i = \frac{\sqrt{2}}{2}$ [closed]

If $i=-1^\frac{1}{2}$, then $2^i$ could be written as $2^{{-1}^{1/2}}$. By the multiplicative law of exponents, this should be equal to $2^{-1/2}$, which is $\frac{\sqrt2}{2}$. This doesn't feel right....
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Show that not all subsets of $[0, 1]$ are Borel-measurable. Find a description of a non-measurable subset ? Hint: use the result about non-existence of shift-invariant measures on $([0, 1],\mathcal P([... 0 votes 0 answers 41 views ### An incomplete proof of d'Alembert's lemma from Stillwell's Elements of Algebra I'm studying Stillwell's Elements of Algebra. In Section 3.8, he gives states d'Alembert's lemma and provides the following proof thereof with the aim of proving the fundamental theorem of algebra. d'... 7 votes 3 answers 560 views ### Please can someone tell accurately and precisely the actual fallacies of this fake proof that 0.999... ≠ 1.000...? Please can someone tell accurately and precisely the actual fallacies of this fake proof that 0.999... ≠ 1.000... ? Define$F: \{\text{decimals in } [0,1]\} \to \{\text{decimals in }[0,1]\}$by$a.... 63 views

### Is this proof true for 0! = 1 [duplicate]

I see proof below for 0! = 1. Is this true in mathematical scientists' idea? (n+1)! = (n+1)n! → (n+1)! ÷ (n+1) = n! Now if we put 0 to n, we will have: 1! ÷ 1 = ...
I thought of a proof that:- $$i=-1=1$$ Here is the proof :- $$(i)^4=(i^2)^2 \\ = (\sqrt{-1})^4=(\sqrt{-1}^2)^2 \\ = (\sqrt{-1})^4=(-1)^2 \\ = (\sqrt{-1})^4=1 \\ \implies i^4=1 \\ \text{also} \\ -1^... 1 vote 3 answers 109 views ### Where is the error in this "proof" that 1=0? Suppose$$x-2z = 0$$Here is what I did to the equation, by dividing x-2z on both sides,$$\frac{x-2z}{x-2z} = \frac{0}{x-2z} \implies 1 = 0$$I don't understand where I am wrong. 0 votes 2 answers 109 views ### Is there an equivalence between a and b when ab \in H, H \subset G$$ab \in H \iff a \equiv b \pmod H It abides by reflexivity, symmetry and transitivity. Proof of reflexivity: (taken from this site) $H \subset G \\ a,e \in G \\ e = aa^{-1} \in H$ Proof of symmetry:... 