Why are elimination reactions in organic chemistry known as beta eliminations?
In an elimination reaction we typically have a leaving group (denoted by "X" in the figure below),  The carbon that the leaving group is attached to is referred to as the "alpha" carbon.  If a hydrogen is removed from the "beta" carbon, then we have formed an olefin and the reaction is called a beta elimination.



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Sometimes an alpha hydrogen can be removed.  In this case both the hydrogen and leaving group were attached to the same carbon and a carbene is formed.