Subject: advance calculus Topic: the set of real numbers

Need detailed solution, two Items only

P (10) Define the metric d on R? by d( (x1, y1). (x2, y2) ) = max{ |x - x2l. ly1 - y2| ). Verify that this is a metric on R' and for & > 0, draw an arbitrary -neighborhood for a point (x, y) e R2. Success never rests. On your worst days, be good; On your best days, be great; and on every other day, be better. - Carmen Mariano(3) Prove the Generalized Triangle Inequality: if a, a2. . .., a,, 6 R then la, + az + ... +ant s lail + laz| + . ..+ lanl. (Hint: Use the Principle of Mathematical Induction)