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.

1281 questions
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Where is the flaw that led to the fallacy that $x^4 + y^4 = z^4$?

Consider $x^2 + y^2 = r^2$. Then take the square of this to give $(x^2 + y^2)^2 = r^4$. Clearly, from this $r^4 \neq x^4 + y^4$. But consider: let $x=a^2, y = b^2 $and$\,\,r = c^2$. Sub this into the first eqn to get $(a^2)^2 + (b^2)^2 = (c^2)^2$.…
CAF
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2 answers

How did my friend make infinity equal to one?

Infinity means there is an infinite amount of something. Unsing same logic, infinity to the power of anything is infinity itself, because there is nothing larger than infinity. My friend proposed this thing to me. I know it should be wrong, but I…
Max0815
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6 answers

Proof that $0=1$?

I recently saw the following "proof" online, and couldn't pinpoint where the mistake was made: From a well known property, $$1+2+3+\cdots = -\frac{1}{12}.$$ Multiplying both sides by $-1,$ we get $$-1-2-3-\cdots = \frac{1}{12}.$$ We can thus…
user389427
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2 answers

Disprove why 0 ∉ Z

Disprove this A value x is said to be an integer when floor(x) = x, where x ∈ ℝ floor(x)/x = 1 Therefore floor(x)/x ∈ Z, where x ∈ ℝ And since 0 ∈ ℝ From the definition of an integer, floor(x)/x ∈ Z, where x ∈ ℝ if 0 ∈ Z, floor(0) =…
Andrew Kor
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1 answer

Factoring cos, and other trig functions

EDIT: I misattributed the solution to factoring. The teacher in fact used a the trig identity: $\cos(A+B) = \cos(A)\cos(B) - \sin(A)\sin(B)$ I apologise for the time wasted on my expediant attempt at factoring trig. I am now more educated on trig…
Thomas J.
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1 answer

What is wrong with this proof of $i = 0$?

This is a proof I made a year ago and at that time, I didn't see any problems with it. Could anyone point out what is wrong here? Consider the following expresion: $(-1)^{(4n+3)/2}$, where $n \in \Bbb Z_+$. We have that: …
Lê Thành Đạt
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1 answer

Why does 2 equal 1?

A friend showed me this proof: Proof: 2 = 1 $$Let \space x= y$$ Multiply both sides by x: $$x^2= xy$$ Subtract $y^2$ from both sides: $$x^2-y^2= xy-y^2$$ Factor: $$(x+y)(x-y) = y(x-y)$$ Cancel out $(x-y)$ from both sides: $$(x+y) = y$$ Simplify…
user14069
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3 answers

Bogus prove of the irrationality of $\sqrt{\frac{1}{2}}$.

I need help figuring out my mistake. Proof. Proving by contradiction that $\sqrt{\frac{1}{2}}$ is irrational. Suppose $\sqrt{\frac{1}{2}}$ is rational so: $\sqrt{\frac{1}{2}}=\frac{m}{n}$. Where $m/n$ are in lowest terms. Squaring both sides and…
Rafa U U
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