Sunday, July 23, 2006

zero divisors

This is a common mistake students make. For instance,


Some will divide both sides by x, and then obtain x=1. But this will result in a loss of a solution to the equation. Weird things start to happen when we divide through by a root (or zero). Perhaps we confuse students in the following case:

sinx =cosx, hence tan x =1.

The student will be confused. Why is it in the latter case we can divide both sides by cosx, yet in the former we cannot divide both sides by x?

Hence I think this example will show to students what is going on.

Why all numbers are equal to zero.

Let x=0. Dividing both sides by x, we have 1=0. So multiplying both sides by 2, we get 2=0, similarly 3=0,4=0 etc, hence all numbers are equal to zero.

Let the class figure out the mistakes themselves.



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