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robertdeniro
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Homework Statement
let A represent the family of linear functions (ie. mx+b) on [0, 1] with distinct slopes
show that if A is equicontinuous, then the absolute value of the slopes are bounded, that is |m|<=C, for all functions in A
Homework Equations
The Attempt at a Solution
equicontinuous means for given e>0, can find &>0 such that |f(x)-f(y)|<e for |x-y|<&
|f(x)-f(y)|=|m(x-y)|<e
if i divide through by |(x-y)| then I am in trouble, since x and y could be arbitrary close
any help?
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