Delta

I have hard time trying to understand why we say that delta for calls can be only between 0 to 1 and the delta for puts can be -1 to 0.

Why cant we say that delta can be 2 for example?

Is there a trick to remember what the greeks mean?

Think about it as the slope of a line and look at the payoff graphs for a long call and short call

Better still, answer this question: if the price of the stock went up $1, who in their right mind would pay an extra $2 for the right to buy it?

As long as you can remember Delta and Gamma, the others are really intuitive to recall. Simple rule of thumb that worked for me is to use alliteration based on the first letters… T heta --> T ime, R ho --> R isk Free Rate, V ega --> V olatility.