Proof
Assume that { ai: i ∈ I } and { bj: j ∈ J } are both bases, with the cardinality of I bigger than the cardinality of J. From this assumption we will derive a contradiction.
Read more about this topic: Dimension Theorem For Vector Spaces
Famous quotes containing the word proof:
“When children feel good about themselves, it’s like a snowball rolling downhill. They are continually able to recognize and integrate new proof of their value as they grow and mature.”
—Stephanie Martson (20th century)
“There is no better proof of a man’s being truly good than his desiring to be constantly under the observation of good men.”
—François, Duc De La Rochefoucauld (1613–1680)
“Right and proof are two crutches for everything bent and crooked that limps along.”
—Franz Grillparzer (1791–1872)