I'm likely not following the standard protocol with this question.
I don't want the answer. I would like to figure it out on my own, but I'm not sure where to start. This is the question proposed by the professor:
Suppose A is non-empty, and that f: A -> B is onto.
How would you explain that there is a function g: A -> B, assuming that were true?
Now, if I'm reading this, I think that f = g, which is why this is confusing.
But... Thinking about any function, there could be infinitely many equations that are equal to each other.
Just, for example, let's say f(x) = x + 17 and g(x) = x(1 + x) - x^2 + 17
These two equations are equivalent.
I feel like I'm rambling on, but if someone could give me a small hint, I'd appreciate it. I'm not sure if I'm sniffing in the right direction or not.
I don't want the answer. I would like to figure it out on my own, but I'm not sure where to start. This is the question proposed by the professor:
Suppose A is non-empty, and that f: A -> B is onto.
How would you explain that there is a function g: A -> B, assuming that were true?
Now, if I'm reading this, I think that f = g, which is why this is confusing.
But... Thinking about any function, there could be infinitely many equations that are equal to each other.
Just, for example, let's say f(x) = x + 17 and g(x) = x(1 + x) - x^2 + 17
These two equations are equivalent.
I feel like I'm rambling on, but if someone could give me a small hint, I'd appreciate it. I'm not sure if I'm sniffing in the right direction or not.