Where has this proof gone wrong? ∞= 1/0

[member 587159]

I stand behind the correctness of the logic in #7: If $\infty$ is an element in the field and has the property that $\frac{1}{\infty}$ = 0 then 1=0.

Indeed, I agree as well to this. There is even a field axiom, called the non-triviality axiom, that forbids that $0 = 1$.

 

[Mark44]

From post #7 (with underlining added by me):

If $\infty$ were a member of the field of real numbers and if one agreed that $\frac{1}{\infty}=0$ then one could proceed to prove nonsense. For example...

In the post above jbriggs444 continues to the nonsense result that 1 = 0.

Then how you reason that x(x-1)=0 isn't proof of 1=0 while in #7 it is?

A shorter version of what jbriggs444 said in post #35.
If x(x - 1) = 0, then we can conclude that x = 0 or x = 1. x can be one of these values but not both. There's no way we can conclude that 0 = 1 from this.

Since we seem to be beating a dead horse here, I'm closing this thread.