Dividing by Zero: What's the Mistake?

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Discussion Overview

The discussion revolves around the mathematical concept of dividing by zero, specifically addressing a mistake made in an algebraic manipulation that leads to an erroneous conclusion. Participants explore the implications of this mistake in the context of solving equations and the validity of certain algebraic steps.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant presents an algebraic expression and suggests that either a false equality (2=1) or a condition (a^2 - ab = 0) must hold, implying a misunderstanding of division by zero.
  • Another participant points out that dividing by a variable that could be zero (in this case, x) leads to the loss of potential solutions, emphasizing the dangers of such operations.
  • A later reply humorously acknowledges the oversight in not recognizing the implications of dividing by zero.
  • One participant explicitly states that the mistake lies in assuming a=b and consequently a^2=ab, which leads to an undefined operation in mathematics.

Areas of Agreement / Disagreement

Participants generally agree that dividing by zero is problematic and leads to errors in mathematical reasoning. However, there is no consensus on the broader implications or the specific nature of the mistake in the original algebraic manipulation.

Contextual Notes

The discussion highlights the importance of recognizing when division by zero occurs and the potential loss of solutions in algebraic equations. Participants do not resolve the specific mathematical steps involved in the original claim.

Who May Find This Useful

Individuals interested in algebra, mathematical reasoning, and the conceptual pitfalls associated with division by zero may find this discussion relevant.

Hernaner28
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What's the mistake here? hehe

http://a7.sphotos.ak.fbcdn.net/hphotos-ak-snc6/64102_341098562596296_100000884664248_973353_615500462_n.jpg
 
Last edited by a moderator:
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##2(a^2-ab) = 1(a^2 - ab)##
Therefore either ##2 = 1## or ##a^2 - ab = 0##
And ##a^2 -ab## is equal to 0, of course.
 
Say you wanted to solve the quadratic [itex]x^2=x[/itex]. You wouldn't begin by dividing through by x because that assumes [itex]x\neq 0[/itex]. If x=0 then you've just lost that solution.

In short, dividing by zero is bad.
 
Hmm I see... it was stupid from me not realising that.. lol :D

Thanks!
 
Don't try this at home...

spikedmath-089-dont-try-this-at-home.png
 
In the first line, you say a=b
and therefore a^2=ab. a^2-ab=0.
You are dividing by zero even though it's not defined in mathematics. That's the mistake... :D
 

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