math set theory logic

The complex number 0 + i0 is the additive identity for the set of complex numbers. 0 + i0 is called the additive identity for the complex number. Z + (0 + i 0 ) = a + i b + (0 + i 0) = (a + 0) + i (b + 0) = a + i..

Introduction - A set of numbers arranged in a definite order according to some definite rule is called a sequence . Sequences have wide applications. For example, the amount of money in a fixed deposit in a bank, over a number of years increases in a sequenc..

Real Numbers - The union of the set of rational numbers and irrational numbers forms the set of real numbers. Q = {rational numbers} = {irrational numbers} Then = R = {real number..

A set of numbers arranged in a definite order according to some definite rule is called a sequence. or A sequence is a function whose domain is the set N of natural numbers. It is customary to denote a sequence by a letter 'a' and the image a(n) or t(n), n N under 'a' by a ..

We must prove two statements. If x A and x B then, by the statement "two sets A and B are different if there exists an element which belongs to one set but not to the other" and by hypothesis, A = B is contradicted. Thus A B. Similarly B A. If A B, th..

Question: For any two sets A and B, prove that A' - B' = B - A. Answer: ..

If every element of A belongs to a set B, and every element of B belongs to C, then clearly every element of A belongs to C. In other words A B and B C then A C..

Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex number system consists of the set of a..

Introduction - Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex number system consists of the ..

Let A be any set. In order to prove that f A we must show that there is no element of f which is not present in A. And since f contains no element at all, no such element can be found out. Hence f A...