Why is 1 not equal to 0 in this proof?

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    Eqautions Precalculus
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Discussion Overview

The discussion revolves around a proof that incorrectly concludes that ##1 = 0##. Participants analyze the steps of the proof to identify where the error occurs, focusing on the implications of dividing by zero and the validity of the mathematical operations involved.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that dividing by zero in the proof leads to a false conclusion, stating that including a false statement allows for proving any statement.
  • Another participant emphasizes that the proof uses ##1 = 0## to derive ##1 = 0##, indicating a circular reasoning flaw.
  • Several participants discuss the implications of the quadratic equation ##x^2 - x = 0##, which has solutions ##x = 0## and ##x = 1##, but does not imply that ##1 = 0##.
  • There is a discussion about the nature of multiplicative inverses and the invalidity of dividing by zero, with one participant questioning the phrasing of a previous explanation regarding multiplicative inverses.
  • Another participant explains that the proof's structure leads to an apparent paradox by manipulating the variable ##x##, ultimately leading to a division by zero.
  • One participant attempts to clarify the reasoning behind the division by zero and the inability to cancel zero in equations, reinforcing the idea that such operations are undefined.

Areas of Agreement / Disagreement

Participants generally agree that the proof contains a critical error due to division by zero, but there is no consensus on the clarity of explanations or the specific phrasing used in the discussion.

Contextual Notes

Some participants express confusion regarding the definitions and implications of mathematical operations, particularly concerning division by zero and multiplicative inverses. The discussion reflects varying levels of understanding and attempts to clarify these concepts.

  • #61
mark2142 said:
(And somebody said it’s proving 1=0 by assuming 1=0. I didn’t get that.)
##25\dfrac{m}{s}## is a quantity of ##25## meter per second. It says what happens within the timespan of one second, namely a change in location of ##25## meter. It normalizes time. One second becomes the unit, i.e. ##1## second = ##1##.

By writing ##\dfrac{x}{x-1}## you introduced the unit ##x-1## which thus is treated like ##1## wheras it still equals ##x-1=1-1=0.## In this sense, you treated ##1## as ##0##. You made ##1## second ##0## seconds.
 
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  • #62
jbriggs444 said:
This is a new predicate that we can get from the previous one by squaring both sides
You mean multiplying by ##x## on both side.
 
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  • #63
This divide by 0 was a joke / trick we used to play on the younger kids at school when I was a teenager. And that was a long time ago! We used to set them up with the basics and say look, this proves 1 = 0 and watch as they approached the maths teacher for help.

Why are we still discussing this in a TWO page thread?! Dividing by zero is just not allowed. End of.

And remind yourself of when it was posted here...
 
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  • #64
PS people my age may remember that The Who released a single in 1971 called "wont get ****** again" :wink:
 
  • #65
DrJohn said:
This divide by 0 was a joke / trick we used to play on the younger kids at school when I was a teenager. And that was a long time ago! We used to set them up with the basics and say look, this proves 1 = 0 and watch as they approached the maths teacher for help.

Why are we still discussing this in a TWO page thread?! Dividing by zero is just not allowed. End of.

And remind yourself of when it was posted here...
No. This is exactly why math in school does not work. Instead of providing any insights, it's simply forbidden. This is not how education works, at least not on PF. Why is it forbidden? You only offer: "because it is". Truth is, the why question can be answered on many levels, and we did not even touch all of them!

Shut up and calculate might work in quantum physics, but it does not work in mathematics. Not even at school, as can be seen at any school of your choice.
 
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  • #66
fresh_42 said:
No. This is exactly why math in school does not work. Instead of providing any insights, it's simply forbidden.
When I was at school I could see for myself that division by zero was problematic. I don't see any deficiency in my reasoning in those days that required advanced abstract mathematics. I certainly wasn't guilty of "shut up and calculate". Quite the opposite!
 
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  • #67
Since this thread has obviously turned into a general mocking about why we discuss it at all, I will close it by now. The original question has been answered on many levels anyway.
 

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