Irrational number

 An irrational number is a real number that cannot be expressed as a fraction of two integers, where the denominator is not zero. In other words, an irrational number cannot be represented in the form a/b(b=/0) Additionally, irrational numbers cannot be exactly represented as terminating or repeating decimals.

Irrational numbers have decimal expansions that neither terminate nor repeat. They go on infinitely without showing a regular pattern. The most famous example of an irrational number is the square root of 2. which cannot be expressed as a fraction and has a non-repeating, non-terminating decimal expansion:

[ \sqrt{2} = 1.414213562373095048801688724209... \]

Other well-known examples of irrational numbers include Euler's number, the mathematical constant pi and the golden ratio (\(\phi\)). These numbers have important mathematical properties and appear in various mathematical and scientific contexts.

Sure, here are a few examples of irrational numbers:

1. Square root of 2 

2. Euler's number ( e):

    e = 2.718281828459045235360287471352... 

3. Pi :

   pi = 3.141592653589793238462643383279... 

4. Golden ratio (phi ):

   phi = 1.618033988749894848204586834365... 

5. Euler-Mascheroni constant ( gamma ):

   gamma = 0.57721566490153286060651209... 

6. The natural logarithm of any positive rational number that is not a perfect power of (e), for example, ln(3)).

These numbers have decimal expansions that do not terminate or repeat, and they cannot be expressed as fractions of two integers.