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For example, a geometric mean (corresponding to a logarithmic distance metric) is more appropriate for strictly positive but otherwise unbounded quantities.
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This replacement can have profound physical consequences, most particularly the spectrum of a quantity (i.e., the numerical values it can possess) can become discretized where it was previously continuous, or bounded where it was previously unbounded, and quantities can be forced to obey a Heisenberg uncertainty principle.
It is not that I have to compare sides in order to ascertain the size of an angle, but rather that our conception of an angle entails the notion of a space contained, as it were, between two lines that meet at a point and we cannot 'think' of a 'mere angle' in the sense of an unbounded spatial quantity.
But there is no reason to believe such a recipe can be implemented, because it requires either the measurement or the preparation of a Turing-uncomputable real-valued quantity with unbounded precision.
At this time, the concept of decidability at issue was that of effective decidability in principle – i.e. decidability by a rule governed method (or effective procedure) each of whose basic steps can be individually carried out by a finitary mathematical agent but whose execution may require an unbounded number of steps or quantity of memory space.
The light tails of the normal distribution allow one to accept the unbounded support as a reasonable approximate description of bounded physical quantities.
Considering the characteristic mentioned in Section II that the content name of NDN are variable and unbounded, 2 million name prefixes from DMOZ [14] and Alexa [15] are analyzed to determine the quantity of MBF used in on-chip memory.
Unbounded chatter begets unbounded despair.
His generosity seemed unbounded.
The possibilities seem unbounded.
A man of "unbounded imagination".
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com