Prove that {1,...,10}X{1,...,15} is finite using only the definition of a finite set.
Defn.: "a set S is finite if either S is the empty set (well obviously not!) OR S is equivalent to the set {1,2,3,...,n} for some positive integer n.
Prove that {1,...,10}X{1,...,15} is finite using only the definition of a finite set.
Defn.: "a set S is finite if either S is the empty set (well obviously not!) OR S is equivalent to the set {1,2,3,...,n} for some positive integer n.
Consider a,b) \to \left[(a-1)+10\times (b-1) +1\right] " alt="fa,b) \to \left[(a-1)+10\times (b-1) +1\right] " />
Then the smallest value takes is , and the largest is , the image of distinct elements of are distinct. Thus we have points in the range and points in the image, and the image is: .
Now turn this into a formal demonstration.
CB
Yes I do understand 1-to-1 & onto (mapping)...Most of our proofs in the last couple weeks have involved bijection....how does this relate to whether or not it's finite (or infinite)...I have already defined my domain & codomain (see previous entry)... f: domain--->codomain. What is f?...graphically it's a solid rectangle therefore how is it 1-to-1? (the cartesian product)....I need help!