Hi, I need some help with understanding bijective functions.
Is the function f(a,b) = (a+1,b) for all (a,b) bijective? I think not because x is not equal to y. Can some please help me with this?
Also similar to this,
f(a,b) = a-1 for all (a,b). Is this function onto or bijective?
Thnaks alot.
Hello kuracYes, if the domain is the whole of . You can think of as a lattice of points in the plane with integer coordinates. The function , then, maps a point onto its immediate neighbour 1 unit to the right. So it's both one-to-one and onto.
Presumably, this function is from to ?f(a,b) = a-1 for all (a,b). Is this function onto or bijective?
If so, it will certainly be onto, because .
But it's not one-to-one, because for a given value of , there are infinitely many possible values of for which . So it is not bijective.
Grandad