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I take it, it's a more proper interpretation of the words.
In that case, math is riddled with such inconsistencies upfront: take an expression as simple as , which for the limit of gives you as valid two opposing extremes:
and . Both extreme opposites are equally true at the exact same point.
Inconsistency is avoided in cases like that by limiting the domain of the function to non-zero values and categorizing the limit as being undefined.
I hadn't thought about it in these terms, but that's an explicit sacrifice of completeness for the sake of consistency.
Inconsistency is avoided in cases like that by limiting the domain of the function to non-zero values and categorizing the limit as being undefined.
But then we can always avoid any inconsistency by limiting the results to the domain of consistency. Yet this is an interesting venue of thought: if the definition of a broken math is that there is no way to define a domain of consistency, that would make said "broken math" even more consistent than math itself.
Inconsistency and falsifiability aren't the same kind of thing, at least not as I understand it.
Falsifiability means we can potentially demonstrate a claim to be false: i.e. we can find a contradiction that results from the claim. If a contradiction is found, then we reject the claim.
Inconsistency would mean that we can show that a claim and its opposite are both true: i.e. A is true and not-A is true.
Inconsistency actually destroys the premise of falsifiability because the contradiction no longer tells us anything.