Can Anyone Explain the 1=2 Trick I Was Shown?

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Discussion Overview

The discussion revolves around a mathematical trick that purportedly "proves" that 1 equals 2. Participants explore various invalid proofs, their implications, and the educational value of such tricks.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses curiosity about a specific trick that demonstrates 1=2 and seeks information on it.
  • Another participant suggests looking up 'Invalid Proofs' on Wikipedia and mentions the abundance of such proofs available online.
  • A participant notes that many of these tricks rely on the invalidity of dividing by zero and encourages creating one's own proof.
  • One participant provides an example of an invalid proof involving algebraic manipulation that leads to the conclusion 1=2, highlighting the division by zero issue.
  • Another participant expresses disdain for these tricks, arguing that they are repetitive and suggest that time could be better spent on other mathematical topics.
  • A contrasting viewpoint is presented, emphasizing the potential inspirational value of such tricks for young learners and their role in sparking interest in mathematics.

Areas of Agreement / Disagreement

Participants express differing opinions on the value of the 1=2 trick. While some find it repetitive and unworthy of attention, others argue for its potential to inspire interest in mathematics among students. No consensus is reached on the overall value of these tricks.

Contextual Notes

Participants reference the reliance on dividing by zero in the proofs, which is a critical point of contention. The discussion includes various examples and personal opinions, but no formal resolution or agreement on the merits of the tricks is established.

Tido611
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I was once shown a cool little trick that "proved" 1=2 and i was wondering if anyone knew what it was or where i could find it, thanks.
 
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I just typed 1 = 2 in the Wikipedia search box and it led me to the page for 'Invalid Proofs'. You might also want to google it.
 
There a thousands of 'em, all relying on the fact that dividing by 0 is not allowed. Just devise your own.
 
[tex]x^2 - x^2 = x^2 - x^2[/tex]

[tex]x(x-x)=(x-x)(x+x)[/tex] Supposedly, the (x-x)'s cancel out, though it equals zero so you can't divide by it.

[tex]x= x+x[/tex]

In other words, 1=2
 
Tido611 said:
I was once shown a cool little trick that "proved" 1=2 and i was wondering if anyone knew what it was or where i could find it, thanks.

I generally despise such tricks, because as mentioned above, once you see one, you have pretty much seen them all. There are apparently over 36 million hits on Google using the term '"1=2" proof'. You could always spend the time on other things in mathematics than this :-p
 
Oh, come on, u don't need to despise them. It could be of great benefit to kids out there who for their first time had seen something unusual. This might inspire them to become the next person to solve riemann's conjecture or unifry all forces of nature. Just like Andrew Wiles who was inspired during his youth to solve FLT.

I first saw this 1=2 business when i was 15, amazed me to no end and made my interest in maths grew even more . haha

EmilK said:
I generally despise such tricks, because as mentioned above, once you see one, you have pretty much seen them all. There are apparently over 36 million hits on Google using the term '"1=2" proof'. You could always spend the time on other things in mathematics than this :-p
 

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