A metric space is a set M together with a distance function ρ(x,y) that represents between elements and y of the set M. The distance function must satisfy the (i) ρ(z, y) > 0 and ρ(x,y)-0 if and only if x y; (iii) ρ(z, y) a(x, z) + ρ(z, y) for all x, y, s in M. Let (M. p) be a metric space. A mapping T from M into M is called a contraction if p(Tr, Ty) ap(x, y) for some constant α with 0 a < 1, and all 21.and y in M. 2. For points P (, vi) and P(2/2)i the plane R2 define the "taxicab" metric which is the distance between two points in a city if one travels only along rectangularly- aligned city streets. Prove that (R, ρ) is a metric space by showing that (i), (ii), and (iii) are again satisfied

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.