An infinitesimal hyperreal exists — Carmelics

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An infinitesimal hyperreal exists

Modality & Possibility Proof of definition segments

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1 reason for

2 reasons against

Reasons For

1 perspective

Reason for

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1.An infinite hyperreal a exists such that a > n for every natural number n
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2.The reciprocal 1/a of an infinite hyperreal a exceeds 0 and is smaller than 1/(n+1) for every natural number n
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Reasons Against

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Reason against 1 of 2

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1.Mathematical existence requires either explicit construction or derivation from axioms accepted as ontologically committed, not merely consistency.
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2.The hyperreals exist only relative to a non-constructive ultrafilter whose existence depends on the Axiom of Choice, making their ontological status model-relative rather than absolute.
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3.A quantity that cannot be specified, measured, or distinguished within any physical or computational procedure lacks the determinate existence required for mathematical realism.
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Reason against 2 of 2

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