I feel like a dunce. I can't find the error

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Discussion Overview

The discussion revolves around a video that claims to prove the equation 4=5 using algebra. Participants analyze the steps taken in the proof, particularly focusing on the implications of dividing by zero and the use of variables.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant notes that the equation A*0 = B*0 does not imply A = B, highlighting a flaw in the proof.
  • Another participant argues that the use of variables A, B, and C obscures the issue, suggesting that substituting values makes the error clear.
  • A specific line in the proof is discussed where B - C - A = 0, leading to the conclusion that the manipulation is invalid since it results in 4 \times 0 = 5 \times 0.
  • Several participants emphasize the importance of not dividing by zero in equations, reiterating that the validity of the resulting equation depends on the divisor being non-zero.

Areas of Agreement / Disagreement

Participants generally agree on the error related to dividing by zero, but there is no consensus on the overall validity of the proof or the implications of the variables used.

Contextual Notes

The discussion highlights the importance of understanding the conditions under which algebraic manipulations are valid, particularly regarding division by zero.

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In line 7, B - C - A = 0. The equation A*0 = B*0 does not imply that A = B.
 
The use of A, B and C is to obfuscate what is going on. If you substitute in the values, it is obvious.

Line 7:
[tex]A(B-C-A) = B (B-C-A)[/tex]
He then divided by B-C-A.

But B-C-A = 0, and so Line 7 is nothing more than
[tex]4 \times 0 = 5 \times 0[/tex]
 
I see.
So the lesson learned here is that when deviding both sides of an equation by anything the resulting equation is only valid where that thing ≠0
Thanks.
 
mrspeedybob said:
I see.
So the lesson learned here is that when deviding both sides of an equation by anything the resulting equation is only valid where that thing ≠0
Thanks.
A shorter way of saying that is that you can't divide both sides of an equation by zero.
 

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