Cours Raisonnements (Logics) , Ensembles ( Sets), Applications (Mappings)

Math Online Tom Circle

This is an excellent quick revision of the French Baccalaureat Math during the first month of French university. (Unfortunately common A-level Math syllabus lacks such rigourous Math foundation.)

Most non-rigourous high-school students / teachers abuse the use of :

“=> ” , “<=>” .

Prove by “Reductio par Absudum” 反证法 (by Contradiction) is a clever mathematical logic :

$latex boxed {(A => B) <=> (non B => non A)} &s=3$

Famous Examples: 1) Prove $latex sqrt 2 $ is irrational ; 2) There are infinite prime numbers (both by Greek mathematician Euclid 3,000 years ago)

The young teacher showed the techniques of proving Mapping:

Surjective (On-to) – best understood in Chinese 满射 (Full Mapping)

Injective (1-to-1) 单射

Bijective (On-to & 1-to-1) 双射

He used an analogy of (the Set of) red Indians shooting (the Set of bisons 野牛):

All bisons are shot by arrows from1 or more Indians. (Surjective…

View original post 81 more words


About tomcircle

Math amateur
This entry was posted in math. Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s