Why is this bad logic ?

  • Thread starter dimachka
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  • #26
matt grime
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dimachka said:
ahh, i see what you are saying, so not necessarily reversible, just only allowed to broaden scope, rather than narrow your scope. I can't exactly see how to make a more concrete explanation of this.
steps only have to be reversible if you want to reverse them is the moral of the story, and you did implicitly want to reverse that irreversible example i gave.
 
  • #27
matt grime
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nazgjunk said:
No, by god. Why did I ever think I was too stubborn? You are far worse. I said it "felt" right, which doesn't mean I believe it. In Dutch class, I feel that it should be answer A, but with some reason I have to admit it is B. OK, this is a crappy example, but I hope you get the point.
mathematics isn't about opinions, when a mathematician says that she feels something ought to be true it usually means that they believe it is true but can't prove it. that is the basis from which my reply was written.
 
  • #28
shmoe
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When first defining exponentiation, rational exponents will be defined as [tex]a^{m/n}=(a^{1/n})^m[/tex] for a>=0 (this is after you've show you have a unique positive nth root of a>=0).

The next step is to show that we have [tex]a^{m/n}=(a^m)^{1/n}[/tex], again under the restriction that a>=0. This is the proposition that has gotten you into trouble, but only because you are applying it without the necessary hypothesis that a>=0.

This is where many of these 'condradictions' come from, applying rules where the conditions are not satisfied, like one of the many 1=2 'proofs' that rely on dividing by zero.
 

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