Chat with our AI personalities
70
equal sets with exactly the same elements and number of elements.equivalent sets with numbers of elements
It kind of depends on what "these" sets are.
Things may be correlated without causal relationship or conversely. Consider the Modulus function - that is the value of a number without regard to its sign. Over any domain (-a,a), there is a very strict relationship between x and mod(x), but their correlation is 0. Conversely, I expect that there is a good correlation between my age and the number of TV sets in the world. That is not to say that my getting older is producing more TVs or that TV production is causing me to age. Simply that both of them are correlated to a third variable - time. There can be correlation without such a third variable but, offhand, I cannot think of an example.
Correlation between two variables implies a linear relationship between them. The existence of correlation implies no causal relationship: the two could be causally related to a third variable. For example, my age is correlated with the number of TV sets in the UK but obviously there is no causal link between them - they are both linked to time.