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Laws of truth and derivation

  1. Dec 28, 2011 #1
    I know from linear algebra that you can take two things, and if they are equal to each other then you can simply substitute different variables to develop a proof of a different statement.

    For example take,

    w = a
    w = z + k
    therefore proof would posit that a = z + k

    But my dilemma lies in what my physics book sometimes does. It derives a "proof" by taking two equations and dividing them by each other to attain a different statement.

    For example,

    w = a
    b = k
    [tex]\frac{w}{b}=\frac{a}{k}[/tex]

    ??? This baffles me. What mathematical theorem or algebraic statement lets us derive something by taking two equations and dividing them by each other? There doesn't seem to be any connection or logic between steps.
     
  2. jcsd
  3. Dec 28, 2011 #2

    AlephZero

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    If b is nonzero, you can say
    [tex]\frac w b = \frac a b[/tex]
    and then because [itex]b = k[/itex]
    [tex]\frac w b = \frac a k[/tex]
     
  4. Dec 28, 2011 #3
    Really its that simple? My professor is an idi**. >.< I'm sorry if this offends anyone but he really does no justice to math or physics combined! He forces ideas down our throats and has little to no justifications for many things. /rant
     
  5. Jan 1, 2012 #4

    Fredrik

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    Yes, it's that simple. It's really just the fact that the equality sign means that what you have on the left is the same thing as what you have on the right. Every equality says something like 5=5, and I'm sure you don't doubt that "5=5 and 3=3" implies that "5/3=5/3". (You just have to make sure that you don't divide by zero).

    You're not the first person who has asked this, and you won't be the last. I don't know why teachers don't explain these "obvious" things. They really should.
     
  6. Jan 1, 2012 #5

    jedishrfu

    Staff: Mentor

    the proof is always left to the student. give your prof a break. zen moments come when you look deeply into a problem and the answer becomes obvious.
     
  7. Jan 1, 2012 #6
    Sometimes, it can be difficult to be aware of the need to explain such things, since they seem too obvious to need explanation. But, to a student who doesn't realize it, it can seem like a serious omission.

    Omitting one step in a proof is not the kind of thing you should be upset about. That's the kind of thing you should just ask about.

    What you should be upset about, for example, is when you are confronted with a horrific half-page calculation with no intuition, and then you discover there is a simple concept behind it that makes it all clear and obvious that was obscured by the professor. I'm just guessing a number, here, but that has probably happened over 100 times in my education so far.
     
  8. Jan 2, 2012 #7

    HallsofIvy

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    He expects you to think for yourself? The Bastard!
     
  9. Jan 2, 2012 #8
    I'm sorry no one here really knows my professor. I'm the type that never complains about professors because I self-teach myself everything anyhow. But this professor really rapes math and physics of all its beauty [had him for physics and calculus], everything was very plug and chug. He gave very little intuition, context, concept motivation, etc. etc.. I've seen him completely rape physics of all its beauty that it irritates me.

    And the reason I said that about my professor not being able to explain it to me is that when I try to ask what -insert name here- law or postulate allows you to do that, he is left out of words. He knows how to use things but does not know where things come from, how things come to be, and their context/bigger picture.

    And I wish he would expect you to THINK for yourself, but in his class things are succumbed to rote calculation. Maybe I'm overreacting and should accept the status quo of quality of professors in this age but I had him for two classes this past semester, so that instigated and accelerated my dislike for his teaching habits.


    Professors aren't perfect, but when its a consistent lack of quality then things get a bit irritating. I can self-teach myself a lot of things, look for a simple concept behind something, and search for something in the bigger context but its much more convenient if professors can fill that role from time to time.

    To HallsofIvy and others,

    The last thing I need is for someone to come in class everyday and go by the books [exactly what he did]. I'm perfectly apt in teaching myself. I don't want someone who goes in the class everyday and go example by example in the book and tell me things that I CAN READ myself. That was the basis of my rant.
     
    Last edited: Jan 2, 2012
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