Recently I am reading Philip Marlowe series of Raymond T.Chandler again.
The Long Goodbye, The Big sleep, Farewell, My lovely, The Little Sister,,,
In Japan as the translations by Haruki Murakami became famous,
I am also reading his works.
I love hard boiled detectives by Robert B.Parker, Ross Macdonald, S.Dashiell Hammett,,,
Haruki Murakami is not my favourite author.
However, his translation is very amenable to originals.
In Playback, the statement of
"If I wasn't hard, I wouldn't be alive.
If I couldn't ever be gentle, I wouldn't deserve to be alive. "
is most famous.
His translation is not bad.
2017/05/31
2017/05/09
axiomatic sets 36 (a totally ordered relation)
We have already gotten the equivalent relation.
For a set $\Omega$ and elements $a,b,c\in \Omega$ ,
(1)if $a\sim b$ ,then $b\sim a$ .
(2)for all $a$ , $a\sim a$ .
(3)if $a\sim b$ and $b\sim c$ , then $a\sim c$ .
We get the ordering relation by changing the condition.
The difference is only (1).
(1)if $a\preceq b$ and $b\preceq a$ , then $a\sim b$
(2)for all $a$ , $a\preceq a$ .
(3)if $a\preceq b$ and $b\preceq c$ , then $a\preceq c$ .
Namely, $a\preceq b$ does not always mean $b\preceq a$ .
A totally ordered relation of the set is for any $a,b\in\Omega$ , $a\preceq b$ or $b\preceq a$ is true.
If it is not true, the set is incomparable and called the partially ordered set.
In axiomatic set theory, we often use a pair $(\Omega,\preceq)$ of a set $\Omega$ and a relation $\preceq$ .
(you must note that a relation is also a set. )
For a set $\Omega$ and elements $a,b,c\in \Omega$ ,
(1)if $a\sim b$ ,then $b\sim a$ .
(2)for all $a$ , $a\sim a$ .
(3)if $a\sim b$ and $b\sim c$ , then $a\sim c$ .
We get the ordering relation by changing the condition.
The difference is only (1).
(1)if $a\preceq b$ and $b\preceq a$ , then $a\sim b$
(2)for all $a$ , $a\preceq a$ .
(3)if $a\preceq b$ and $b\preceq c$ , then $a\preceq c$ .
Namely, $a\preceq b$ does not always mean $b\preceq a$ .
A totally ordered relation of the set is for any $a,b\in\Omega$ , $a\preceq b$ or $b\preceq a$ is true.
If it is not true, the set is incomparable and called the partially ordered set.
In axiomatic set theory, we often use a pair $(\Omega,\preceq)$ of a set $\Omega$ and a relation $\preceq$ .
(you must note that a relation is also a set. )