Set Theory and Logic


Confirmation of the Triangle Inequality

Authors: Colin James III

"[T]he triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side." We rewrite this as contradiction F implies tautology T using absolute values of distances: "If qr is not greater than pq with pr, then both qr is greater than pq and qr is greater than pr." Hence the triangle inequality is confirmed as tautologous. Remark: This exercise indirectly speaks to the fact that the vector space is not bivalent.

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[v1] 2018-07-29 12:12:31

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