Indian mathematicians like Brahmagupta (598-670) and Bhaskaracharya (1114-1185) had made contributions to the understanding of the real numbers system and algebra.

**Introduction**

Algebra is a branch of
mathematics in which one expresses relations among quantities by using symbols
to represent these quantities. The symbols are called the *variables*. In this class we shall allow the variables to represent
real numbers only. One can carry out manipulations and computations using
variables just as one does with numbers. That is, one may substitute real
numbers for the variables in the expression and the resulting value will also
be a real number. Once a quantity or a mathematical statement is expressed in
terms of variables, it is possible to substitute specific numerical values for
those variables. This makes algebra a very powerful tool. For this reason the
subject of algebra has very wide application, not only within mathematics, but
also in other disciplines and in real life. The notion of real numbers is
fundamental to the whole of mathematics. The real number system was well
understood only in the nineteenth century. The need for extending the rational
numbers arose quite early in the history of mathematics. Pythagoreans knew that
√2 was not a rational number. Certain
constructions involving irrational numbers can be found in Shulbha Sutras,
which date back to around 800 BCE. Aryabhata (476-550) had found approximations
to *π*.

Indian mathematicians
like Brahmagupta (598-670) and Bhaskaracharya (1114-1185) had made
contributions to the understanding of the real numbers system and algebra. In
his work Brahmagupta had solved the general quadratic equation for both
positive and negative roots.

Bhaskaracharya solved
quadratic equations with more than one unknown and found negative and
irrational solutions. The most important real number zero was the contribution by Indians.

*Rene Descartes *(1596-1650) introduced the term “real” to
describe roots of a polynomial equation distinguishing them from imaginary
ones. A rigorous construction of real number system was due to Richard Dedekind
(1831-1916).

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