Prove that the union of 2 finite sets is finite w/o use of any arithmetic?

Question

No, this isn't homework, yes I really am doing this for fun. While you're at it, could you please explain what equinumerous means I have a definition: a set A is equinumerous to a set b iff there is a one to one function from A onto B, but I'm still a little confuse.

Thanks!

Answer 1

Two sets A, and B are equinumerous if the card(A) = card(B) (A and B have the same number of elements)



If A and B are finite, list the elements of A as {a1,a2,...,an} and B as {b1,b2,..,bm}. Hence A union B has the following as elements: {a1,a2,...,an,b1,b2,...,bm}. Hence, A union B is finite.

Answer 2

Union means AND. When you AND things together you can get the same number of items in the set or fewer. So if you start with two finite sets, the total number of items can be equal to the set with the largest number of items or smaller than the largest down to zero items. (And any number smaller than a finite number is finite.)



Equinumerous means that for each item in one set there is another item in the other set. A function maps an input (the range) to a SINGLE output (the domain). If we say that for each item in A a function will map to B, then we are saying that there are exactly as many items in A as B.

Answer 3

it sounds as if equinumerous is similar to equivalence, whereby two sets are equivalent if they have equal cardinality,i.e. the same number of elements