Hello guys.
First of all good job on making this awesome forum.
Secondly i'd like to ask for some help regarding my calculus exercises.
Here it is:
Prove by induction that |x1 + x2 + · · · + xn(little n)| ≤ |x1| + |x2| + · · · + |xn(little n)| for any n ∈ N and any numbers x1, . . . , xn(little n) ∈ Q.
AND
(a) Use the ordering axioms to show that x 2 < y2 for any x, y ∈ Q with 0 < x < y. (
b) Use the previous result to prove by induction that x^n < y^n for any n ∈ N and any x, y ∈ Q with 0 < x < y. ( I Have solved A, can someone help with b? thanks
First of all good job on making this awesome forum.
Secondly i'd like to ask for some help regarding my calculus exercises.
Here it is:
Prove by induction that |x1 + x2 + · · · + xn(little n)| ≤ |x1| + |x2| + · · · + |xn(little n)| for any n ∈ N and any numbers x1, . . . , xn(little n) ∈ Q.
AND
(a) Use the ordering axioms to show that x 2 < y2 for any x, y ∈ Q with 0 < x < y. (
b) Use the previous result to prove by induction that x^n < y^n for any n ∈ N and any x, y ∈ Q with 0 < x < y. ( I Have solved A, can someone help with b? thanks