$0\leq a

Question

$0\leq a<b,0\leq c<d$, prove $ac<bd$

Just a hint, please... It sounds intuitively obvious, but I need something more rigorous than that.

anonymous · Answer

Well, intuition is usually a pretty good thing to go with...so, let's begin with what's your intuition tell you?

anonymous · Answer

If A is a smaller number than B, but greater than 0, and if C is a smaller number than D, but greater than zero, A*C is going to be smaller than B*D... which is what I'm supposedly trying to prove.

anonymous · Answer

It's annoying when my intuition tells me the answer is intuitive, rather than giving me an intuitive proof "path" to follow.

anonymous · Answer

Oh hey, I got the answer. Nevermind,

anonymous · Answer

I'm so dumb.

anonymous · Answer

lol

anonymous · Answer

np...I wanted to see what your idea was and build off that if it was close to what was neededd.

anonymous · Answer

$0\leq a<b,0\leq c<d\rightarrow0\leq ac<bc,0\leq bc<bd\therefore bd>ac$

anonymous · Answer

Well done.  As I said, intuition is usually a good thing to start with.