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Prove that $-\psi(y) \leq c(x,y) + c(x,\bar y) - \psi(\bar y)$

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#inequality #supremum-and-infimum #monotone-functions #optimal-transport
43
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$f$ is strictly increasing, $f (a) < a$, $ f(b) > b$. Number of solutions to $f(c) = c$.

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#real-analysis #continuity #monotone-functions
74
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Prove the following for the monotonic function $f$ on $[0,1]$ satisfying $f \left (\frac {1} {4} \right ) f \left (\frac {3} {4} \right ) \lt 0.$

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#real-analysis #continuity #solution-verification #supremum-and-infimum #monotone-functions
703
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Is the union of partially ordered sets also partially ordered?

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#elementary-set-theory #relations #order-theory #monotone-functions
61
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Show that $F$ is a monotone function

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#elementary-set-theory #computer-science #relations #order-theory #monotone-functions
66
Views

Economics-utility function

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#functions #economics #monotone-functions #utility
64
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Question of calculus concepts

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#calculus #functions #monotone-functions
48
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Why does this being a finite set mean that it cannot be the case that all element of the sequence are distinct?

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#sequences-and-series #computer-science #order-theory #lattice-orders #monotone-functions
51
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How do we know that $F^{n + 1}(\overrightarrow{\emptyset}) = F(F^n(\overrightarrow{\emptyset}))$?

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#computer-science #order-theory #lattice-orders #monotone-functions #fixed-points
70
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Cardinality of order preserving functions from totally ordered set with dense subset

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#elementary-set-theory #order-theory #cardinals #monotone-functions
106
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Using induction with monotonicity to show that $F^n(\overrightarrow{\emptyset}) \sqsubseteq F^{n + 1}(\overrightarrow{\emptyset})$

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#induction #solution-verification #computer-science #order-theory #monotone-functions
57
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Using induction with monotonicity to show that $F^n(\overrightarrow{\emptyset}) \sqsubseteq \overrightarrow{RD}$

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#induction #solution-verification #computer-science #order-theory #monotone-functions
119
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Monotone Sequence $\frac{n}{n+1}$

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#real-analysis #sequences-and-series #induction #monotone-functions
110
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Compute inf and sup of a set A

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#supremum-and-infimum #monotone-functions #monotone-class-theorem
62
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How to show that the sum of a function is strictly increasing?

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#real-analysis #sequences-and-series #continuity #monotone-functions

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