INTERVALS #intervals

 INTERVAL :   

        

                           Interval is the subset of the real line R.

 There are few kinds of intervals .

  i.  (a,b) = {x/xꜪR,a<x<b}    pronounced as open interval a,b

            This interval containes all the numbers between a and b except a and b.

  ii.  [a,b] = {x/xꜪR,a≤x≤b} . . . . . . .closed interval a,b

            this interval contains all the numbers between a and b together with a and b.

  iii.  (a,b] = {x/xꜪR, a<x≤b} . . . . .  semi left open interval a,b or semi right closed interval                        a,b

           This interval contains all the numbers between a and b together with b only.

  iv.   [a,b) = {x/xꜪR,a≤x<b}  . . .  . . semi left closed interval a,b or semi right open interval                        a,b

                     This interval contains all the numbers between a and b together with a only.

  v.   [a,∞) = {x/xꜪR,x≥ a}  . . .  . . . . closed interval a,infinity  open or closed a,infinity

  vi.  (a,∞) = {x/xꜪR,x>a} . . . . . . . . .open interval a, infinity open or open a,infinity

  vii. (-∞,a] = {x/xꜪR, x≤a} . . . . . . . . open -infinity , a closed    

  viii. (-∞,∞)= {x/xꜪR}   

 

 NOTE  : Since infinity (∞ ) is not a limit point to any intervals and sequences , we put open                  brackets beside infinity in any interval.  

 

* extended real line 

*  Axioms of Real numbers

* fourth dimensional objects

* Euclidean spaces

*  subsets of the real line R.

* Inductive Set

 ^{*  Is infinity (∞ ) a number?}