### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Space and its dimension

A space is said to be of dimension zero, one, two or three as it comprises of a single  point, line, plane or contains points not all of which are co-planers.

‘Space’ shall mean a three -dimensional space.

Some Axioms on Space

(i) Axiom-1:

Space is a non-empty set of points.

(ii) Axiom -2:

If are distinct points in space then and if  is a plane containing then

(iii) Axiom -3:

Given any three non-collinear point in space is exactly one plane  such that

(iv) Axiom -4:

If are two distinct planes in a space and is a point such that then there exists another point  different from such that

CONVEX SET

A subset of a space is said to be a Convex set if, for all . Otherwise it is not a convex set.

(v) Axiom -5:

If is a plane is space then the point of not contianed in are divided into two disjoint non-empty convex sets such that

Note:

If a point belongs to space we also say that the point lies on/in that space.

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