Definition
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[07V]Given two ordered non-empty sets \((X,≤_ X)\) and \((Y,≤_ Y)\), we will say that ”they have the same order type”, or ”order-isomorphic”, or more briefly that they are ”equiordinate” 1 , if there is a strictly increasing monotonic bijective function \(f:X→ Y\), whose inverse \(f^{-1}\) is strictly increasing. The function \(f\) is the “order isomorphism”.