Consider the POSET (P,<). Assume < is a total order, and P has a smallest element, s. Assume that every non- empty subset of P has a greatest element, g. Let f be a function f:P → P such that VxeP, VyeP, if (x

Consider the POSET (P,<). Assume < is a total order, and P has a smallest element, s. Assume that every non- empty subset of P has a greatest element, g. Let f be a function f:P → P such that VxeP, VyeP, if (x

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Consider the POSET (P,<). Assume < is a total order, and P has a smallest element, s. Assume that every non-
empty subset of P has a greatest element, g. Let f be a function f:P → P such that VxeP, VyeP, if
(x <y) → (f(x) < f(y)). Prove or disprove. There exists an element in P such that p < f(p).

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