Find the cardinality of $S=\{(x,y) \in \Bbb R^2 : 2x+3y<5\}$.
Attempt:
I graphed this set, and I noticed that the simpler set $(0,1)^2=B\subset S$, and I thought these two sets had the same cardinality, so I tried to find two injections, there's the easy one $id:(0,1)^2\to S/id:(x,y)\mapsto(x,y)$, but I couldn't find a reverse one...
Besides this problem, can you guys give me some general tips on how to solve these type of problems? Another example is "Find the cardinality of $A=\{graphs\}$.
Hint: All you need is that the cardinality of $\mathbb{R}^2$ is the same as $\mathbb{R}$ which is the same as $(0,1)$. To make this as clean as possible, you may have to use the fact that if there are two injections going each way between two sets $A$ and $B$, then $A$ and $B$ have the same cardinality.