Thread: Show surjective HELP...

Hello, can someone help me show that the following function is surjective (onto)?

f: Z -> G, where Z = integers and G = {10^n : n e Z}

So, we have f(n) = 10^n

Take any y e G. Then y = 10^x for some x.

=> Taking ln of both sides gives x = ln(y)

What do I do from here? Thanks

Hey jzellt.

You can show that each value is unique in the co-domain (also you may want to change ln(y) to log_10(y)).