Friday, April 29, 2011

The end of an era

In a half hour I'll be attending my last math class as a student, possibly for the rest of my life here on earth. (Yes, I am certain there will be math classes in Heaven.  It's gonna be a party--me and my teachers, Galileo, Newton, and Pascal.)

Anyway, in honor of this passage from student to hopefully-teacher, I thought I'd share this little image with you that I like to share with my College Algebra students on the first day of class.  If you can find the error, you get a gold star!

6 comments:

  1. This comment has been removed by the author.

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  2. Fifth Line.

    (a+b)(a-b)=b(a-b) is only true because both sides are multiplied by zero (a-b). It does not make (a+b)=b.

    Its like saying (4x0)=(5x0) - true statement.

    But, it does not follow that 4=5.

    Just because you multiply two things by zero and get zero does not make the two things equal.

    Gold star?

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  3. Josh Blain! You surprise me. Great work. I grant thee a gold star.Some explanation is necessary though...

    From lines 3 to 4, both sides were not multiplied by zero arbitrarily. They were factored, which is legal. The left hand side is the difference of two squares and so gets factored into (a+b)(a-b) and the right hand side has a common factor of b which got factored out. The problem is that in the next line, we "cancel," or DIVIDE by (a-b), which is zero, which is a no-no, for reasons you alluded to in your fantastic example.

    I am impressed!

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  4. I don't understand much of anything of the math but I do understand this is a big deal. Congratulations and have fun!!

    http://stealingfaith.com

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  5. Oddly the first thing I noticed was that your last step was to divide both sides by a, which is also not allowed as we have no guarantee that a is not zero itself! I had the same odd feeling when I finished my last math class here at UNL. It's odd to think that I may never go back and take another math class! Hope the transition to teacher treats you well!

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  6. Very wise, Master Heltibridle, very wise.

    I'm also glad there's someone else to share the shock of possibly never having another math class...

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