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| ====== Playground ====== | ====== Playground ====== | ||
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| ===== Problem 1: Linear Extension ===== | ===== Problem 1: Linear Extension ===== | ||
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| d) Show that $\leq_1$ is a linear extension of $\leq$ if and only if $(A,\leq_1)$ is a total order and the identity function is a monotone function from $(A,\leq)$ to $(A,\leq_1)$. | d) Show that $\leq_1$ is a linear extension of $\leq$ if and only if $(A,\leq_1)$ is a total order and the identity function is a monotone function from $(A,\leq)$ to $(A,\leq_1)$. | ||
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