1. Prove that an ordered field has the LUB property iff it has the GLB property.
I know that I need to prove that if the ordered field has the GLB property, then it has the LUB property, and that if the ordered field does NOT has the GLB property, then it also does not have the LUB...
f: A-->B is a function. A,B are sets.
Let A1, A2 be contained in/equal to A.
f(A1 intersection A2) is contained in OR equal to f(A1) intersection with f(A2). Show that the equality holds if f is an injection.
I know how to prove that it is contained, but not the equal/injection part...
1. Let R be a relation on X that satisfies
a) for all a in X, (a,a) is in R
b) for a,b,c in X, if (a,b) and (b,c) in R, then (c,a) in R.
Show that R is an equivalence relation.
2. In order for R to be an equivalence relation, the following must be true:
1) for all a in X, (a,a) is...