I have played the game "Ori and the Blind Forest definitive edition" on PC.
In easy mode, it took me 22 hours, and in normal mode (on the second lap), 12 hours.
(all skills are unlocked, 87% of maps is cleared, and as the last event finished, the end staffs roll was displayed. )
The game has an old classical 2D action style.
(same as Super Mario, but the motion of "Ori" is quicker than Mario. )
It has very mournful and good BGM and beautiful graphics.
The controls by which "Ori" defeats the enemies, escapes from the traps, and gets to the each goals are much difficult, because a little "Ori" is weak and the trap is not almost able to avoid if you have not already known.
(there are no puzzles, for each goals there is only one way which "Ori" have to choose. )
However, the difficult controls give me a high sense of accomplishment when the quests are completed, and I can feel my game play becomes better and my feeling becomes high and hot.
It is recommended on snowy cold day in winter vacation.
This is the last post in 2016.
I wish you a Merry Christmas and a happy New Year !!
2016/12/20
2016/12/06
axiomatic sets 28 (the number system)
We have seen the system of numbers or the structure of numbers,
where basic elements are the empty set and the axiom of ordered pair.
(1)Natural numbers $\mathbb{N}$ : $\phi,\left\{\phi \right\},\left\{\phi,\left\{\phi \right\} \right\},\cdots$ means $0,1,2,\cdots$ .
(2)Integers $\mathbb{Z}$ : $[(\phi,\phi)],[(\left\{\phi \right\},\phi)],[(\phi,\left\{\phi \right\})],[(\left\{\phi,\left\{\phi \right\} \right\},\phi)],[(\phi,\left\{\phi,\left\{\phi \right\} \right\})],\cdots$ means $0,1,-1,2,-2,\cdots$ .
(3)Rational numbers $\mathbb{Q}$ :
$[([(\phi,\phi)],[(\left\{\phi \right\},\phi)])]=0$ ,
$[([(\left\{\phi \right\},\phi)],[(\left\{\phi \right\},\phi)])]=1$ ,
$[([(\phi,\left\{\phi \right\})],[(\left\{\phi \right\},\phi)])]=-1$ ,
$[([(\left\{\phi,\left\{\phi \right\} \right\},\phi)],[(\left\{\phi \right\},\phi)])]=2$ ,
$[([(\phi,\left\{\phi,\left\{\phi \right\} \right\})],[(\left\{\phi \right\},\phi)])]=-2$ , $\cdots$ .
(4)Real numbers $\mathbb{R} $: the set of all "Dedekind cuts" ($\left\{x\in\mathbb{Q} : x\lt a,a\in\mathbb{Q} \right\}$)
We are not conscious for the making of numbers or the system of numbers.
However, have you ever had a little bit of doubts something like why $\frac{-1}{3}=\frac{1}{-3}$ or the definition of irrational numbers is numbers which is not rational numbers, etc, etc ?
The number system will answer some questions and you will see the rigorousness exists in every fields of mathematics.
It makes us very comfortable and gives much confidence.
*
In these definitions, the relation of $\mathbb{N}\subset\mathbb{Z}\subset\mathbb{Q}\subset\mathbb{R}$ will require one to one correspondence.
where basic elements are the empty set and the axiom of ordered pair.
(1)Natural numbers $\mathbb{N}$ : $\phi,\left\{\phi \right\},\left\{\phi,\left\{\phi \right\} \right\},\cdots$ means $0,1,2,\cdots$ .
(2)Integers $\mathbb{Z}$ : $[(\phi,\phi)],[(\left\{\phi \right\},\phi)],[(\phi,\left\{\phi \right\})],[(\left\{\phi,\left\{\phi \right\} \right\},\phi)],[(\phi,\left\{\phi,\left\{\phi \right\} \right\})],\cdots$ means $0,1,-1,2,-2,\cdots$ .
(3)Rational numbers $\mathbb{Q}$ :
$[([(\phi,\phi)],[(\left\{\phi \right\},\phi)])]=0$ ,
$[([(\left\{\phi \right\},\phi)],[(\left\{\phi \right\},\phi)])]=1$ ,
$[([(\phi,\left\{\phi \right\})],[(\left\{\phi \right\},\phi)])]=-1$ ,
$[([(\left\{\phi,\left\{\phi \right\} \right\},\phi)],[(\left\{\phi \right\},\phi)])]=2$ ,
$[([(\phi,\left\{\phi,\left\{\phi \right\} \right\})],[(\left\{\phi \right\},\phi)])]=-2$ , $\cdots$ .
(4)Real numbers $\mathbb{R} $: the set of all "Dedekind cuts" ($\left\{x\in\mathbb{Q} : x\lt a,a\in\mathbb{Q} \right\}$)
We are not conscious for the making of numbers or the system of numbers.
However, have you ever had a little bit of doubts something like why $\frac{-1}{3}=\frac{1}{-3}$ or the definition of irrational numbers is numbers which is not rational numbers, etc, etc ?
The number system will answer some questions and you will see the rigorousness exists in every fields of mathematics.
It makes us very comfortable and gives much confidence.
*
In these definitions, the relation of $\mathbb{N}\subset\mathbb{Z}\subset\mathbb{Q}\subset\mathbb{R}$ will require one to one correspondence.