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It is not the case that An undefined value is categorically distinct from zero distance, which would entail co-location or identity of position.
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Reasons For
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Reason for
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1.
Both undefined values and zero distance fail to establish differentiation in practice—both describe limiting or boundary cases indistinguishable operationally.
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2.
The claim assumes undefined and zero are competing characterizations, but undefined may simply mean 'zero-distance hasn't been assigned a determinate value yet.'
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3.
Category distinctions require clear criteria; the argument doesn't establish what property differentiates undefined from zero-distance beyond semantic labeling.
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Reasons Against
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Reason against
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1.
Undefined values lack determinate properties; zero distance entails measurable spatial coincidence—these are fundamentally different logical categories.
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2.
Identity of position is a concrete relational fact; indefiniteness is epistemic absence—conflating them commits a category error.
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3.
In formal systems, undefined terms cannot satisfy identity conditions that zero-distance requires, making them categorically distinct.
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