1)Suppose a1, a2,.....,an are denumerable sets. Show that a1Xa2X....Xan is denumberable(a1Xa2X...xan is the set of n-tuples(a1,a2...an),ai is an elember of Ai)

I literally have no idea what that means so any direction would be nice(a1 is a sub 1 btw)

2)a)Suppose 0<=a<b and o<=c<d, prove that 0<=ac<bd

b)0<=a<b then 0<=a^2<b^2

c)if 0<a<b, show that a<rt(ab)<(a+b)/2<b (hint contradiction)