為何學數學 ? (libre office 原稿)

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Chapter 0 : Background

2005http://youtu.be/Ip0hG7FXVgs

:http://teacher.whsh.tc.edu.tw/lichiou/f2blog/index.php?load=read&id=127

The first story is about connecting the dots. If I had never dropped out, I would have never dropped in on this calligraphy class, and personal computers might not have the wonderful typography that they do. Of course it was impossible to connect the dots looking forward when I was in college. But it was very, very clear looking backwards ten years later.

Again, you can't connect the dots looking forward; you can only connect them looking backwards. So you have to trust that the dots will somehow connect in your future. You have to trust in something your gut, destiny, life, karma, whatever. This approach has never let me down, and it has made all the difference in my life

My second story is about love and loss.

My third story is about death.

Boolean

Integer

Set

Relation

Computing

?

V.S.

Why ?

Why


- JPEG






cosine transform
JPEG

eix

eix = cos(x)+i sin(x)

f(x)

Fi ai , bi

(Halting Problem)

- (1)

?

- (2)

I P

()

Halting Problem :

P I

Halting Problem

InputProgram P

InputProgram P

P as Input

Output

H(P,P)

If H(P,P)=halt then loop forever

If H(P,P)=loop foreverthen halt

Halting Problem

H(P,I)="halt" if P(I) halt
="loop forever"if P(I) loop forever

H K

K(P) = if H(P,P)="halt" then loop forever
else halt

H(K,K) ?

Halting Problem

If H(K,K)="halt"K(K) loop forever

If H(K,K)="loop foreverK(K) halt

H is not correct anyway.

Java

String K(String P) { if H(P, P) == halt { while (true) { } } else { }}

If K(K) loop forever H(K,K) = halt

If K(K) halt H(K,K) halt





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FPGA...

TCP/IP...

2D3D...

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PTL (2002 2008 )(2002)

BasicPascalCVBHTML/JavaScript/ASP
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