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2 results

  • 8 - Real Analysis

  • from Part III - Where Are the Paradoxes?
  • Zach Weber, University of Otago, New Zealand
  • Book:
    Paradoxes and Inconsistent Mathematics
    Published online:
    08 October 2021
    Print publication:
    21 October 2021, pp 230-255

  • Summary

    The target of this chapter is to give some rudiments of(paraconsistent) real analysis, a dissection of the linear continuumas that which has no gaps. Axioms for the reals as a totally orderedcomplete field are given and developed, with philosophicalconsiderations about the nature of points. Focus is on the topologyof the real line, establishing the general principle at stake: thatif a change occurs, it must occur somewhere. This is confirmed atthe intermediate value theorem. Along the way, the (continuous)sorites paradox is “recaptured,” the existence ofinfinitesimal quantities is floated, and a theorem is proved about“splitting” geometric points.