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There is also a second-derivative test: if the derivative of a function is zero at a point, then the function will have a relative maximum or minimum if the second derivative at that point is less than or greater than 0, respectively, the test failing if it equals 0. Relative maxima can also occur at points at which the derivative fails to exist, and these points must also be tested.
Note first that the thesis of serious actualism can be expressed as the thesis that all properties are existence-entailing; there is no possible world in which something has a property but fails to exist in that world.
It is well known that the ML estimator exists when the data is non-separable, but fails to exist when the data is separable.
When a punishment allocation fails to exist for some agent, dynamic games in which agents gradually reveal their evidence implement a larger set of outcomes.
In the case when such an optimal sequence fails to exist, we present an O(m) greedy algorithm to obtain a suboptimal sequence based on some important properties of the overhead factors.
Similar reasoning shows that any other false proposition fails to exist.
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Could an existing substance have failed to exist?
No existing substance could have failed to exist.
Spinoza concludes that for any existing substance, it could not have failed to exist nor can it cease to exist.
It is commonly accepted that there are two sorts of existent entities: those that exist but could have failed to exist, and those that could not have failed to exist.
So remember kids, clean up - or fail to exist!
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com