A report onMathematical analysis, Calculus and Real number

These theories are usually studied in the context of real and complex numbers and functions.

- Mathematical analysis

Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis.

- Mathematical analysis

In mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits.

- Calculus

The development of calculus in the 18th century used the entire set of real numbers without having defined them rigorously.

- Real number

The completeness property of the reals is the basis on which calculus, and, more generally mathematical analysis are built.

- Real number

For example, an infinitesimal number could be greater than 0, but less than any number in the sequence 1, 1/2, 1/3, ... and thus less than any positive real number.

- Calculus

Mathematics

Mathematics is an area of knowledge that includes such topics as numbers (arithmetic, number theory), formulas and related structures (algebra), shapes and the spaces in which they are contained (geometry), and quantities and their changes (calculus and analysis).

This was a major change of paradigm, since instead of defining real numbers as lengths of line segments (see number line), it allowed the representation of points using their coordinates (which are numbers).