Euclidean spaces no relation finite set
In mathematics, semi-infinite objects are objects which are infinite or unbounded in some but not all possible ways.In ordered structures and Euclidean spaces
Generally, a semi-infinite set is bounded in one direction, and unbounded in another.  For instance, the natural numbers are semi-infinite considered as a subset of the integers; similarly, the intervals 
  
    
      
        (
        c
        ,
        ∞
        )
      
    
    {\displaystyle (c,\infty )}
   and 
  
    
      
        (
        −
        ∞
        ,
        c
        )
      
    
    {\displaystyle (-\infty ,c)}
   and their closed counterparts are semi-infinite subsets of 
  
    
      
        
          R
        
      
    
    {\displaystyle \mathbb {R} }
  .  Half-spaces are sometimes described as semi-infinite regions.
Semi-infinite regions occur frequently in the study of differential equations. For instance, one might study solutions of the heat equation in an idealised semi-infinite metal bar.
A semi-infinite integral is an improper integral over a semi-infinite interval.  More generally, objects indexed or parametrised by semi-infinite sets may be described as semi-infinite.Most forms of semi-infiniteness are boundedness properties, not cardinality or measure properties: semi-infinite sets are typically infinite in cardinality and measure.
no relation