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adding content on real line
It is sometimes convenient to have a set of numbers that ''does'' include infinity. For example, in computer programming, "real arithmetic" is often done by a specific system defined by standard IEEE 754-1985; this system is built in to modern processor chips. It provides for values which print out as INF and -INF and which participate in arithmetic as if they were numbers. Thus, division by zero, which was often an error that stopped calculation on older machines, can be a legal operation which simply produces a +INF or -INF result. The system of numbers implemented in IEEE 754 is known in mathematics as the "affinely extended real numbers."
It is sometimes convenient to have a set of numbers that ''does'' include infinity. For example, in computer programming, "real arithmetic" is often done by a specific system defined by standard IEEE 754-1985; this system is built in to modern processor chips. It provides for values which print out as INF and -INF and which participate in arithmetic as if they were numbers. Thus, division by zero, which was often an error that stopped calculation on older machines, can be a legal operation which simply produces a +INF or -INF result. The system of numbers implemented in IEEE 754 is known in mathematics as the "affinely extended real numbers."
==Real line==
The real numbers can be thought of as a [[line]], called the '''real line'''. Each real number represents a point on the real line. However, it is a mistake to think of the real line as a row of individual points, like beads. There is no real number “just to the right” of a given real number. This is because the real numbers, like the rational numbers, are a [[dense set]], so points accumulate around each other.<ref>http://abstractmath.org/MM/MMRealNumbers.htm</ref>
The real line is useful as a [[coordinate system]] for [[graph]]ing [[functions]]. Thus, the [[x-axis]] and [[y-axis]] are both instances of the real line. The real line is the basis for geometric [[measurement]]s, and more generally for ideas in [[metric topology]].
==Notes and references==
==Notes and references==
{{reflist}}
[[Category:Mathematics]]
[[Category:Mathematics]]