Explanation:
Irrational number
In mathematics, an irrational number is any real number which cannot be expressed as a
fraction a/b, where a and b are integers,
with b non-zero, and is therefore not a rational number. Informally, this
means that an irrational
number cannot be represented
as a simple fraction. Irrational numbers are precisely those real numbers that
cannot be represented as terminating or repeating
decimals. The best-known irrational numbers are π, e and √2.
The number is irrational.
The
real line
In mathematics, the real line, or real number line is the line whose points are the real numbers. That is, the real line
is the set R of all real numbers, viewed as a geometric space, namely the Euclidean space of dimension one.
Just like the set of real numbers, the real line is usually
denoted by the symbol R (or alternatively, the letter "R" in
blackboard bold). However, it is sometimes denoted R^{
}in
order to emphasize its role as the first Euclidean space.
http://en.wikipedia.org/wiki/Real_line
The above explanation is copied from Wikipedia, the free
encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported
License.
(Our solved example in mathguru.com uses the below concept. This
is our own explanation and has not been taken from Wikipedia.)
To represent (say) on number line
Steps of Construction
(1) Mark the distance x units from a fixed point A and obtain a
point B such that AB = x units.
(2) From B, mark a distance of 1 unit and mark the new point as
C.
(3) Find the midpoint of AC and name it as M.
(4) Taking MC as the radius, draw a semi circle.
(5) Draw a line perpendicular to AC passing through B and
intersecting the semi circle at D.
(6) Draw an arc with Center B and radius BD, which intersects
the number line in E.
(7) Then, E represents.