Mixing
A proof on interval order
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Let $X$ be a nonempty finite set and $≻$ a binary relation on X. We say that $≻$ is an interval order if $x≻y$ and $x'≻y'$ imply either $x≻y'$ or $x'≻y$, for every $x$,$y$,$x'$ and $y'$ in $X$.
Prove that $≻$ is an interval order iff there exist two real functions $f$ and $g$ on $X$ such that $x≻y$ iff $f(x)>g(y)$ for every $x$ and $y$ in $X$.
set-theory
asked 56 mins ago
qwert3
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Let $X$ be a nonempty finite set and $≻$ a binary relation on X. We say that $≻$ is an interval order if $x≻y$ and $x'≻y'$ imply either $x≻y'$ or $x'≻y$, for every $x$,$y$,$x'$ and $y'$ in $X$.
Prove that $≻$ is an interval order iff there exist two real functions $f$ and $g$ on $X$ such that $x≻y$ iff $f(x)>g(y)$ for every $x$ and $y$ in $X$.
set-theory
asked 56 mins ago
qwert3
12
New contributor
qwert3 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Let $X$ be a nonempty finite set and $≻$ a binary relation on X. We say that $≻$ is an interval order if $x≻y$ and $x'≻y'$ imply either $x≻y'$ or $x'≻y$, for every $x$,$y$,$x'$ and $y'$ in $X$.
Prove that $≻$ is an interval order iff there exist two real functions $f$ and $g$ on $X$ such that $x≻y$ iff $f(x)>g(y)$ for every $x$ and $y$ in $X$.
set-theory
asked 56 mins ago
qwert3
12
New contributor
qwert3 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Let $X$ be a nonempty finite set and $≻$ a binary relation on X. We say that $≻$ is an interval order if $x≻y$ and $x'≻y'$ imply either $x≻y'$ or $x'≻y$, for every $x$,$y$,$x'$ and $y'$ in $X$.
Prove that $≻$ is an interval order iff there exist two real functions $f$ and $g$ on $X$ such that $x≻y$ iff $f(x)>g(y)$ for every $x$ and $y$ in $X$.
set-theory
set-theory
asked 56 mins ago
qwert3
12
New contributor
qwert3 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 56 mins ago
qwert3
12
New contributor
qwert3 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 56 mins ago
qwert3
12
New contributor
qwert3 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 56 mins ago
qwert3
12
asked 56 mins ago
qwert3
12
12
New contributor
qwert3 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
qwert3 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
qwert3 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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qwert3 is a new contributor. Be nice, and check out our Code of Conduct.
qwert3 is a new contributor. Be nice, and check out our Code of Conduct.
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