Avoiding dividing by 0 in an equation

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What was the method for modifying an equation to avoid dividing by zero?
I think it involved adding 1 somewhere, then removing the error that creates later.


For example,

a / b = c

It is possible that one of the values placed in the b variable could be 0. How would the equation be modified so that dividing by zero wouldn't occur?
 
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If b is a variable that could be zero, then a/b=c doesn't even make sense in the first place.

What is the context of this?
 
Its a commonly left out detail, sometimes considered obvious, sometimes completely forgotten. When you have a fraction a/b, b can not equal zero. Its a restriction placed on b in order for the division to be defined.
 
The only way to "modify" the equation a/b= c so that you can avoid dividing by 0 is to remove the division entirely: a= bc.
 
Of course there's the possibility that in the limit a->0 and b->0 ; a/b equals a real number and the eqn. makes sense. Hard to tell without context.
 
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I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

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