Suppose that a function f is a subadditive prove that if f(0)=0 and if f is continuous at x=0 then f is continuous on all of R ?

how can i solve it ?

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- Apr 24th 2010, 08:37 AMneset44Subadditive Proof
Suppose that a function f is a subadditive prove that if f(0)=0 and if f is continuous at x=0 then f is continuous on all of R ?

how can i solve it ? - Apr 24th 2010, 03:40 PMTikoloshe
A function is continuous at a point if . Another characterization of continuity at (which is useful in your case) is that . ( of course is defined as

I would use the subadditivity of f along with the above characterization to show continuity at an arbitrary point.