In physics, approximations of real numbers are used for extended real number system, or by requiring the counting of an infinite number of events.
2.
The affinely extended real number system turns into a totally ordered set by defining-\ infty \ leq a \ leq + \ infty for all a.
3.
Examples are the closed intervals of real numbers, e . g . the unit interval [ 0, 1 ], and the affinely extended real number system ( extended real number line ).
4.
Since the supremum and infimum of an unbounded set of real numbers may not exist ( the reals are not a complete lattice ), it is convenient to consider sequences in the affinely extended real number system : we add the positive and negative infinities to the real line to give the complete totally ordered set ( " ", " ), which is a complete lattice.
5.
The limit of a sequence of points \ left ( x _ n : n \ in \ mathbb { N } \ right ) \; in a topological space " T " is a special case of the limit of a function : the domain is \ mathbb { N } in the space \ mathbb { N } \ cup \ lbrace + \ infty \ rbrace with the induced topology of the affinely extended real number system, the range is " T ", and the function argument " n " tends to + ", which in this space is a limit point of \ mathbb { N }.
मोबाइल