The Answer to Algebra Witchcraft

This is the answer to my puzzle, Algebra Witchcraft.  If you haven't read that yet, here's a link, then you can come back here at any point.

The answer is:

Well, the algebra is perfectly well formed.  So if you were looking for a mistaken or slight of hand, there isn't one.  That's what the clue was about - its not a trick.

So if it isn't a trick, what gives.

Given:    a=b

We can substitute b throughout with a.  This gives the following:

From that we can see that each of the steps are self evidently true.  That is:

Step One
Step Two
Step Three
Step Four
Step Five
Step Six

So its not the algebra.

But did you spot what happened in Step 5 and Step 6.  The only way that they can resolve is if:

a = 0

And there's the answer.  The algebra is fine, it's just applied to a single special case.  


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