Other Meanings
Sometimes "almost disjoint" is used in some other sense, or in the sense of measure theory or topological category. Here are some alternative definitions of "almost disjoint" that are sometimes used (similar definitions apply to infinite collections):
- Let κ be any cardinal number. Then two sets A and B are almost disjoint if the cardinality of their intersection is less than κ, i.e. if
- The case of κ = 1 is simply the definition of disjoint sets; the case of
- is simply the definition of almost disjoint given above, where the intersection of A and B is finite.
- Let m be a complete measure on a measure space X. Then two subsets A and B of X are almost disjoint if their intersection is a null-set, i.e. if
- Let X be a topological space. Then two subsets A and B of X are almost disjoint if their intersection is meagre in X.
Read more about this topic: Almost Disjoint Sets
Famous quotes containing the word meanings:
“An amoeba is a formless thing which takes many shapes. It moves by thrusting out an arm, and flowing into the arm. It multiplies by pulling itself in two, without permanently diminishing the original. So with words. A meaning may develop on the periphery of the body of meanings associated with a word, and shortly this tentacle-meaning has grown to such proportions that it dwarfs all other meanings.”
—Charlton Laird (b. 1901)
“Words differently arranged have a different meaning, and meanings differently arranged have different effects.”
—Blaise Pascal (1623–1662)