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!

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ReplyDeleteFifth Line.

ReplyDelete(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?

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

ReplyDeleteFrom 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!

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

ReplyDeletehttp://stealingfaith.com

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!

ReplyDeleteVery wise, Master Heltibridle, very wise.

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