[rsp1984]

This. It's even more obvious in linear algebra where mathematicians routinely start with the premise "Ax = b", even if there is no solution x that would satisfy the equation exactly.

[maho]

I disagree: "Ax = b" is a statement. It does not need to be true. This is quite useful and often used for "proofs by contradiction".

[rsp1984]

I see it being used all over the place as a starting point to solve for x, even if A is non-square and/or x ends up being a least squares solution.

[jcranberry]

The supposition in instances like these is one expressing a notion of equivalence, whether or not an equality results in a contradiction doesnt mean that the meaning of the symbol has changed.

[sirclueless]

I vaguely remember writing question marks over equality signs when one was using an equals sign as a proposition.