If I have some set $A$ and a subset $B$, where the cardinality of $A$ is greater than $B$, can I have either a bijection, surjection, or injection?
In other words, lets say I have some sequence where every element is in the set of Natural numbers, and $f(x+1) > f(x)$. Then I have some subset of the natural numbers $B$ such that it coins only the even elements of the natural numbers. Can this be a bijection or surjection?