Mathematics Stack Exchange
Mathematics Stack Exchange

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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Where is wrong in this proof

Suppose $a=b$. Multiplying by $a$ on both sides gives $a^2 = ab$. Then we subtract $b^2$ on both sides, and get $a^2-b^2 = ab-b^2$. Obviously, $(a-b)(a+b) = b(a-b)$, so dividing by $a - b$, we find $a+b = b$. Now, suppose $a=b=1$. Then $1=2$ :)
a d
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Through any $n$ distinct points on a plane we can draw a straight line.

I can't understand what is wrong with this paradox. How we should strictly mathematically explain it? Mathematical induction: 1. The basis: $n=1,n=2$. Through any two (one) points on a plane we can draw a straight line. 2. The inductive…
Mike
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Fake proof that there don't exist complicated numbers

So there's this false proof going around that I can't seem to find now that says that complicated numbers don't exist. So let me explain what it's about (I've added some technical details of my own, but the idea is the same). Definition A number $a…
Martín Forsberg Conde
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What's wrong with this proof?

$$e^i = (e^i)^{(2\pi/2\pi)} = (e^{2\pi i})^{1/2\pi} = 1^{1/2\pi} = 1.$$ I first saw this one many years ago, written on the wall of a bathroom stall in the Princeton University math department.
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Find a mistake type of math problems

I am interested in the problems where the formulation of the problem has some kind of mistake in it and as a consequence gives unexpected answer. Can't explain it better than this example: For example: $4^2 = 4 \cdot 4 = 4+ 4 + 4+4$ (sum $4$…
Winten
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What's wrong with that proof?

What wrong with this proof? $(-1)=(-1)^{\frac{2}{2}}=(-1)^{2\times \frac{1}{2}}=\sqrt{1}=1$ then $1=-1$
mohamez
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The value of $(-0.1)^{-0.1}$

I saw a video about how the answer for this is complex because- $(-0.1)^{-0.1}$ $\frac{1}{(-0.1)^{0.1}}$ $\frac{1}{(-0.1)^\frac{1}{10}}$ $\frac{1}{\sqrt[10]{-0.1}}$ $\sqrt[10]{-0.1} \;\epsilon \;\mathbb{C}$ But if I write 1/10 as …
Code1248
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Can this really happen?

Yesterday, while scribbling on the back page of my maths copy, I accidentally came across this If $ x\in R\ $ and $ x+x+x+.....\infty = m $ where $ m $ is any real number. Then we can write $ x+x+x+.....\infty = m $ $\Rightarrow $ $ x+m=m $ $…
Aniruddha
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Why if $a =b$ then $a = 0$ is not a correct statement

Bogus Claim: If $a$ and $b$ are two equal real numbers, then $a = 0$ $a = b$ $a^2 = ab$ $a^2 - b^2 = ab - b^2$ $(a-b)(a+b) = (a-b)b$ $a + b = b$ $a = 0$ I found this in my proof handouts, and correct me if I'm wrong,but is it wrong because after…
August
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I've formulated a proof, but also a counterexample?

show that f(x) is injective. $f(x)= \frac{x^2}{1+x^2}$ if $f(x)=f(y)$ then $\frac{x^2}{1+x^2}=\frac{y^2}{1+y^2}$ $(x^2)(1+y^2)=(y^2)(1+x^2)$ $x^2+x^2y^2=y^2+x^2y^2$ $x^2 = y^2$ $x = y$ but $f(1)=f(-1)$ due to the square roots. Where did I go…
Osuynonma
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Where's the foolish part ? Prove that 0/0 = 2

I've been across this on the web: \begin{align} \frac{0}{0} & = \frac{100-100}{100-100} \\ & = \frac{10^2-10^2}{10(10-10)} \\ & = \frac{(10-10)(10+10)}{(10)(10-10)} \\ & = \frac{(10+10)}{10} \\ & = \frac{2}{1} \\ & = 2 \end{align} Of course this is…
Thomas Ayoub
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Does square difference prove that 1 = 2?

I was mathematically shown 1 = 2 by a function that states the following $$x^2-x^2 = x^2-x^2 $$ $$x(x-x)=(x-x)(x+x)$$ dividing by $(x-x)$ we get... $$x=x+x$$ $$ x=2x$$ $$1=2$$ I can see that mathematically he was right, but for sure that…
fady taher
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Explain what is wrong with the following "proof" by induction.

Basically, there's so much going on in this problem that I don't even understand it. I've read it about one million times, but it still isn't making sense to me. Any hints would be appreciated... Claim: Let $p$ be a polynomial of degree $n ≥ 1$ that…
thisisourconcerndude
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Best basic algebra examples to show students that proof by example is not sufficient

Often, students will try to 'prove' a propositon by checking some examples and 'concluding' that it will be true for all $n \in N$. I'm looking for some good, non-trivial examples from highschool and lower college mathematics showing that checking…
Floyd
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Positive quadratic function in $\mathbb{R}$ for all real numbers requires a negative determinant

The following simple exercise appears in the book "Undergraduate Topology" by Robert H. Kasriel (Dover publication 2009). I know you can find proofs in any elementary algebra book, yet I made the effort proving this trying to use the most elementary…
Bufo Viridis
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