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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What is wrong with this proof there is no $\omega$-th worldly cardinal

Call a cardinal $\kappa$ worldly iff $V_\kappa\vDash ZFC$. Let $\kappa_\alpha$ be the $\alpha$th worldly cardinal, i.e. the least worldly cardinal such that $\{\beta\lt\kappa_\alpha|\beta\text{ is worldly}\}$ has order-type $\alpha$. Since the class…
Master
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Wrong theorem - The number 1 is the largest integer

I have a theorem and its proof. I am trying to find the flaw in this wrong theorem. Theorem : The number 1 is the largest integer. Proof -> Suppose the conclusion is false. Then let $ n> 1$ be the largest integer. Multiplying both sides of this…
user9026
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Problem with derivative of x^n

I have a problem regarding the proof of the derivative of x^n using first principles. Here's my proof. D is for delta y = x^n y + Dy =(x+Dx) ^n So Dy = (x+Dx) ^n - x^n We can factor this as (x +Dx -x) (x^(n-1)+....+Dx^(n-1)) …
IAS0601
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Difficutly recognising flaw in putative theorem

I'm trying to answer a textbook question from page 188 of How To Prove It, second edition by Daniel J. Velleman, but I can't figure it out. Consider the following putative theorem. Theorem? Suppose $R$ is a relation on $A$, and define a relation…
HarrisonO
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I can't spot the mistake. What's happening?

Let x and y be equal integers, x or y isn't equal to 0 or 1. We have the following: $x=y$ -subtract x to both sides $x-x=y-x$ $0=y-x$ -divide y²-x to both sides $\frac{0}{y^2-x}=\frac{y-x}{y^2-x}$ $0=y$ -divide y to both sides $0=1$…
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Where is the flaw in this proof that "any algebra variable does not equal any number"?

A friend of mine showed me this proof to demonstrate that any algebra variable does not equal any number. his proof relies on this idea $$0\neq1$$ $$0x\neq1x$$ $$0\neq1x$$ $$0\neq x$$ Full Proof: $$\forall n (n \in…
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Compatibility of probabilistic axioms and arithmetic - Fermat's Last Theorem

From this answer I followed a link to this description of a proof which cites from this original source. A "proof" of Fermat's Last Theorem is presented using manipulation of the equation according to theory of probabilities and De Morgan's laws,…
Wildcard
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A proof that zero equals one via limits

Could someone explain where and why this "proof" falls apart? $\lim_{x\to\infty} x = \infty = \lim_{x\to\infty} x - 1$ implies \begin{align*} 0 &= \lim_{x\to\infty} 0 \\ &= \lim_{x\to\infty} (x - x) \\ &= \lim_{x\to\infty}x - \lim_{x\to\infty} x…
user20354139
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What's wrong with the Proof?

Theorem 1.8 Let A,B,X be points on a line having coordinates a,b,x respectively. If $X \notin \overrightarrow{AB}$ and a < b then x < a. Proof: We assume the A,B,X are points on a line with coordinates a,b,x respectively with a < b and that$ X…
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Why can a = b imply 2 = 1?

$$ a = b $$ $$ a^2 = ab $$ $$ a^2 - b^2 = ab - b^2 $$ $$ (a+b)(a - b) = b(a - b) $$ $$ a + b = b $$ $$ 2b = b $$ $$ 2 = 1 $$ Does the self-reference to the original formula make this path of argument invalid? I am confused as to what's going on…
CinchBlue
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Math: amounts and a proof about amounts

I would like to proof or disprove the following 2 statements, if any is not true I need to find an example which disproves it. X and Y are amounts and f: X --> Y This is a question where I have trouble with. Can anyone give me an advice how to…
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Why is this proof of $i = -1$ wrong?

I know that $-7^2 = -49$ Therefore $\sqrt{-49} = -7$ Because $\sqrt{-1} = i$ we can then expand it to $\sqrt{-49} = -7 = 7i$ And therefore $-7 = 7i$, divide both sides by 7 and you get $-1 = i$ And I know that is not true, because $i = \sqrt{-1}$.…
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What did I do here? This can't be right... ($i = -1$)?

I was messing around in Geometry class today and found a very odd 'proof'. It relies on only two facts, $1^2=1$ and $i=\sqrt{-1}$ From here I did this: $$i = \sqrt{-1}$$ $$i^2 = -1$$ $$-i^2 = 1$$ therefore, since $-i^2 = 1$ and $1^2 =…
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Can someone please explain how the proof below is wrong for $9=3$?

Where is the error? $-27=-27$ $81-108=9-36$ $9^2 - 2\cdot 9\cdot6 = 3^2 - 2\cdot3\cdot6$ $9^2 - 2\cdot9\cdot6 + 6^2 = 3^2 - 2\cdot3\cdot6 + 6^2$ $(9-6)^2 = (3-6)^2$ $9-6 = 3-6$ $9=3$
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Everything is equal

This bothers me for a while: Proof $a = b$ $$a=b$$ $$b=a$$ $$a+b=b+a$$ $$a+b=a+b$$ $$0 = 0$$ This looks like a proof for $a=b$, but it shouldn't work like this. But i can't put my finger on why it's wrong.
Dorus
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