Why is f ( x ) = x continuous?

Question

Why is             f              (        x        )              =          x       continuous?

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For every number a in             (      0      ,      ∞      )      , we have             lim              x        →        a                    x        =          a      . That is the definition of continuous at a.At 0, we have             lim              x        →                  0          +                            x        =          0       which is the definition of continuous from the right at 0.So             x       is continuous on             [      0      ,      ∞      )      .            lim              x        →        a                    x        =          a       can be proven using the definition of limit.

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