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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
by rsp1984 9y ago
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 9y agoI 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 9y agoI 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 9y agoThe 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 9y agoI vaguely remember writing question marks over equality signs when one was using an equals sign as a proposition.