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:
“In the reproof of chance
Lies the true proof of men.”
—William Shakespeare (1564–1616)
“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)
“There are some persons in this world, who, unable to give better proof of being wise, take a strange delight in showing what they think they have sagaciously read in mankind by uncharitable suspicions of them.”
—Herman Melville (1819–1891)