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…
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Mathtuition88 