What is Adherent point in Real Analysis ?
Definition. Let S be a subset of ℝ . A point x ∈ ℝ is said to be an adherent point of S if every neighbourhood of x contains a point of S. It…
Read more
Principle of induction
Let S be a subset of ℕ such that (i) 1 ∈ S, and (ii) if k ∈ S then k +1 ∈ S. Then S = ℕ . Proof. Let T= ℕ - S. We prove that T= Φ. Let …
Read more
Show that 0 is a characteristic root of matrix A if and only if A is singular
source: adobe stock Solution: Let 0 be the characteristic equation of matrix A. Then implies ⌈A-ΥI⌋=0 Hence | A |=0 is singular. Converse…
Read more
What is Vector Space ?
source: adobe stock Let V be a non-empty set and addition is an internal binary operation denoted by '+' that is a map from V x V → V whic…
Read more
Definition of Mapping , injective mapping, Bijective mapping , Constant mapping, Identity mapping , inverse mapping
source:adobe stock Mapping Let A and B be two non - empty sets. A mapping f from A to B is a rule, that assigns to each element x of a d…
Read more
Definitation of Finite and Infinite Sets, Equal Sets , Incomparable Sets, Universal Set , Disjoint Sets
source: adobe stock Finite and Infinite Sets A set is said to be a finite set if either it is empty or it contains a finite number of elements; othe…
Read more
TRANSFORMATION OF RECTANGULAR AXES
source: adobe stock Types of the transformation of axes T here are three distinct types of transformation of co-ordinates, namely (i) translation (…
Read more
LOGARITHMIC FUNCTION OF A COMPLEX NUMBER
source: adobe stock Let z be a non-zero complex number. Then there always exists a complex number w such that = z. w is said to be a Logarithm of z…
Read more
EXPONENTIAL FUNCTION OF A COMPLEX NUMBER
source: adobe stock The function of a real variable x, is called the exponential function of a real variable x. is For a complex variable z=x+i…
Read more
DEMOVIRE'S THEOREM
source: adobe stock If n is an integer, positive or negative and Θ is a real number ( COSΘ +iSINΘ) ∧ n = cosnθ+isinnθ If n is a fraction, posi…
Read more
Social Plugin