I need to prove the following:
Suppose P
is a statement about positive integers and c is some fixes positive integer. Assume i) P(c) is true; and ii) for every m>=c, if P(m) is true, them P(m+1) is true. Then P is true for all n>=c.
I know that in order to show this it will be a prove by contradiction, my teacher said that it is similar to the one where we start with P(1) is true. Thus we assume that there exist an n>=c such that P is false. What i have is the following:
Thus there exist an m such that P(m) is false. Because of i) we know that m can not equal c. Thus m-c>=c. From here is do not know what to do??
Suppose P
is a statement about positive integers and c is some fixes positive integer. Assume i) P(c) is true; and ii) for every m>=c, if P(m) is true, them P(m+1) is true. Then P is true for all n>=c.I know that in order to show this it will be a prove by contradiction, my teacher said that it is similar to the one where we start with P(1) is true. Thus we assume that there exist an n>=c such that P
is false. What i have is the following:Thus there exist an m such that P(m) is false. Because of i) we know that m can not equal c. Thus m-c>=c. From here is do not know what to do??