會唔會有兩個set A同B
A 嘅 cardinality 大過 B
但 A 嘅 dimension 細過 B
吾不懂數學2019-04-29 21:59:56
唔可能, intuitively個set多左野自然要用多D野去形容佢
以finite dimensional vector space爲例, 如果 dim A < dim B, 我地可以embed A 落 a subspace of B
e.g. A 的 basis 係 {a_1, a_2, ..., a_m}
B 的basis係 {b_1, b_2, ..., b_m, ..., b_n}
我地可以construct 一個linear transformation f: A -> B such that
f(a_i) = b_i
咁樣就有個injection, 即係cardinality of A最多會係cardinality of B