introduction to set theory

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A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For example, x - y, a + 3b, x 3 + 4y etc. are binomials. We know that, For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical manner in terms of combinatorial coeffi..

If m is a positive integer, a x a x a . m times is written as a m . a is called the base and m is the power. We read it as "a raised to the power m". The power is also called "the index" or "the exponent". When the power or index is a fraction say then and it is a surd of order n. In this chapter w..

The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical Induction is a principle by..

Let us consider the marks obtained by four students in Physics, Chemistry and Biology for the first unit test. We have represented the data in rows and columns. (i) Rows show the marks obtained by each student. (ii) The columns show the marks in Physics, Chemistry, Biology obtained by each student...

You are familiar with factors and products in the case of numbers. For example, 8 is the product of 4 and 2. 4 and 2 are called the products of 8 . Similarly, the algebraic expression a x b x c = abc can be written as 1.a.b.c or 1.ab.c or 1.bc.a or 1.ac.b or 1.abc. 1, a, b, c, ab, bc, ac, abc are a..

Lets say there are 6 frogs and 2 crabs in a pond. We can compare the number of frogs to the number of crabs in two different ways: How many more frogs than crabs are there? or How many fewer crabs than frogs are there? The answer to both the questions is same i.e. 6-2=4. There are 4 more frogs than..

This chapter takes us much further and adds to our already existing knowledge about Ratio and Proportion. We will have to use many of the algebraic manipulations learnt earlier, use them with expertise to solve problems in this chapte..

We use specific number of digits to denote an exact value of a number for required accuracy. The digits used for such a purpose are called significant figure..

The theory of finite sets is, arguably, a definition of Combinatorics. In particular, certain combinatorial topics (e.g. Ramsey theory) have important direct analogues in "combinatorial" set theory. Since Axiomatic Set Theory..