Okay i need some help understanding what induction is..I know that for some open statement you must prove thatif the smallest element in the set is true... every element in that universe is true... I know that you use the basis step for the smallest element. and for the induction step you must prove that if s(k) is true . you must prove that s(k+1) is true. But what i don't understand is how would i prove that? like i see some statements and for the induction step. they add (k+1) to the statement and then just simplify it. but how does that prove that the statement is true? is there any other method than just adding (k+1)? edit: Also ... i keep seeing something called the induction hypothesis...... can anyone explain it without making it too confusing?