The error is that the "..." denotes an infinite sum, and such a thing does not exist in the algebraic sense. The usual way to make sense of adding infinitely many numbers is to use the notion of an infinite series: We define the sum of an infinite series to be the limit of the partial sums. (So the notion of convergence from analysis is involved in addition to algebra.)
Not all algebraic rules generalize to infinite series in the way that one might hope. When they fail, it is because something fails to converge. In this case, what fails to converge is the series that should appear between the two lines in the middle of the "proof":
Indeed, this series fails to converge because the
sequence of partial sums 
oscillates between 
and 
and does not converge to any value.
Reddit
reddit.com › r/modern_family › gottlob alister's last theorem s10e21
Gottlob Alister's Last Theorem S10E21 : r/Modern_Family
April 5, 2023 - Dividing both sides by 1 - 1 [= 0] gives us 0/0 and 0/0, which is not a valid operation in any world. The conjecture "x + y = y" doesn't follow in any way, and is inherently untrue. This isn't a theorem, and it doesn't "suggest" anything.
Nathanmarz
nathanmarz.com › blog › proof-that-1-0-using-a-common-logical-fallacy.html
Proof that 1 = 0 using a common logical fallacy - thoughts from the red planet - thoughts from the red planet
Theorem 1. 0x = 0. Proof. 0x + 0x = (0 + 0)x = 0x. By Lemma 1, 0x = 0.
YouTube
youtube.com › watch
"PROVE" 0 = 1 Using Integral Calculus - Where Is The Mistake? - YouTube
This is a false proof of why 0 = 1 using a bit of integral calculus. Can you figure out where the mistake is?My blog post for this video:https://wp.me/p6aMk-...
Published August 10, 2017
GetYarn
getyarn.io › yarn-clip › cf26dd25-9ec3-440d-8a18-f266d5fdd704 › gif
YARN | Gottlob Alister wrote a proof showing that zero equals 1. | Modern Family (2009) - S10E21 Commencement | Video gifs by quotes | cf26dd25 | 紗
Modern Family (2009) - S10E21 Commencement clip with quote Gottlob Alister wrote a proof showing that zero equals 1. Yarn is the best search for video clips by quote. Find the exact moment in a TV show, movie, or music video you want to share.
Simon Singh
simonsingh.net › books › fermats-last-theorem › what-is-the-last-theorem
What is the Last Theorem? | Simon Singh
The more that mathematicians tried, the more they failed, and the more desirable a solution became. The Last Theorem was a source of frustration, but it also had a lighter side. In the 1980s a piece of graffiti appeared on New York’s Eighth Street subway station.
Zditect
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HMC Math
math.hmc.edu › funfacts › one-equals-zero
One Equals Zero! – Math Fun Facts
x = y. Then x2 = xy. Subtract the same thing from both sides: x2 – y2 = xy – y2. Dividing by (x-y), obtain x + y = y. Since x = y, we see that 2 y = y. Thus 2 = 1, since we started with y nonzero. Subtracting 1 from both sides, 1 = 0.
YouTube
youtube.com › watch
🧠 Can You Spot the Mistake? Fun Math Puzzle: Does 0 = 1? 🎉 - YouTube
🧠 Can You Spot the Mistake? Fun Math Puzzle: Does 0 = 1? 🎉In this fun and puzzling video, I present a mind-boggling mathematical "proof" that seems to show...
Published April 25, 2011
YouTube
youtube.com › john hush
Proof that 0 = 1 - YouTube
Mr. John Hush proves, using an infinite series, that 0 = 1.
Published December 14, 2011 Views 1M
Quora
quora.com › How-do-I-prove-0-1
How to prove 0=1 - Quora
Answer (1 of 10): We knew that- 0–0 = 1–1 so now let's take 0 and 1 both as common 0(1–1) =1(1–1) 0 = 1(1–1)/(1–1) 0 = 1 Hence proved . You can solve it by this method but it's wrong as 0 and 1 can’t be equal . (^_-)-☆ :) :D
Wikipedia
en.wikipedia.org › wiki › Mathematical_fallacy
Mathematical fallacy - Wikipedia
January 26, 2026 - after which the antiderivatives may be cancelled yielding 0 = 1. The problem is that antiderivatives are only defined up to a constant and shifting them by 1 or indeed any number is allowed.
Academia.edu
academia.edu › 2822337 › Spectral_methods_for_discontinuous_problems
(PDF) Spectral methods for discontinuous problems
October 11, 2025 - S. Abarbanel, D. Gottlieb and E. Tadmor, Spectral methods for discontinuous problems, in "Numerical Methods for Fluid Dynamics II", ed. by K.W. Morton and M.J.
YouTube
youtube.com › university of oxford
What is Fermat's Last Theorem? - YouTube
Professor Sir Andrew Wiles of Oxford University has been awarded the 2016 Abel Prize – one of the highest honours in mathematics – for his proof of Fermat’s ...
Published March 15, 2016 Views 244K
Alistairsavage
alistairsavage.ca › mat1362 › notes › MAT1362-Mathematical_reasoning_and_proofs.pdf pdf
Mathematical Reasoning & Proofs MAT 1362 Winter 2025 Alistair Savage
Case 2: c < 0. In this case −c = 0 −c ∈N. Thus ... In either case we arrive at a contradiction, and so our proof is complete. Example 2.25. Let us prove that 8n −3n is divisible by 5 for all n ∈N. We will prove this ... Since 81 −31 = 8 −3 = 5 = 5 · 1, we see that P(1) is true. Now assume that P(n) is true for some n ∈N. ... Since 8n + 3m ∈Z, we see that 5 divides 8n+1 −3n+1. Sometimes we wish to start an induction at an integer other than 1. Theorem 2.26 (Principle of mathematical induction: first form revisited).
Pleacher
pleacher.com › mp › mhumor › onezero2.html
one equals zero
Proof that zero equals two (Using Algebra) Given that a and b are integers such that a = b, Prove: 0 = 2 1. a = b 1. Given 2. a - b - 2 = a - b - 2 2. Reflexive Prop. of = 3. a(a - b - 2) = b(a - b - 2) 3. Multiplication Prop. of = 4. a2 - ab - 2a = ab - b2 - 2b 4. Distributive Property 5. ...
YouTube
youtube.com › ahmed abdrabou
كيف تثبت ان (Proof that (0 = 1 - YouTube
كيف تثبت ان (Proof that (0 = 12=1 proof errorhow to prove 2=31=2 proof flaw1=2 proof quora1+1=2 prooffind the error in the proof that 2 = 1can you prove 2=11...
Published January 4, 2021 Views 239
Tlcusc
tlcusc.com.br › tzc8s94a › gottlob-alister-last-theorem-0=1.html
gottlob alister last theorem 0=1
Lecture Notes in Computer Science ... . no. Modern Family (2009) - S10E21 Commencement clip with quote Gottlob Alister wrote a proof showing that zero equals 1....
Wikipedia
en.wikipedia.org › wiki › Fermat's_Last_Theorem
Fermat's Last Theorem - Wikipedia
3 weeks ago - In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases ...
Austms
austms.org.au › wp-content › uploads › Gazette › 2006 › Mar06 › Mar06.pdf pdf
Austms
We are professional and industrial mathematical scientists, data scientists, actuaries and financial mathematicians, educators, researchers, and students. We include Fellows of the Academy of Science, Prime-Minister’s Prize winners, even Fields Medallists. We are united by our shared passion ...