SENTENCE: That couple has an affinity for dancing.
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An affine combination is a linear combination of vectors in Euclidian space in which the coefficients add up to one.
Euler introduced the term affine (Latin affinis, "related") in 1748 in his book "Introductio in analysin infinitorum." Felix Klein's Erlangen program recognized affine geometry as a generalization of Euclidean geometry.
Every plane has 3 or more. There is a projective (or affine) plane with only 3 points.
In ordinary geometry (as opposed to affine geometry), a plane MUST consist of an infinite set of points.
An infinite number in a Euclidean plane - which is the "normmal" plane. Some selected numbers in the finite or affine planes (but you need to be studying projective geometry to come across these).