Question

How to prove that two functions are one-one and onto?

Answer 1

one to one means that there is a unique range value for any given domain value; onto means that every element in the range is used ....

Answer 2

by contradiction, show that these hold or do not hold

Answer 3

Yeah, but is there a formula or anything to prove it?

Answer 4

there is no formula, there is only logical proof. Either show a counterexample to prove false, or show by contradiction that it must be true

Answer 5

if m:f -> g and is 1-1onto, then m^-1:g -> f

prolly a bad write up ....

Answer 6

do yo have 2 specific functions? or is this a general abstraction?

Answer 7

Show that f:N->N, given by

is both one-one and onto.