Question about limits and inequalities

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AxiomOfChoice
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If you have

[tex] T < M + \epsilon,[/tex]

where [itex]\epsilon > 0[/itex] is arbitrary, does this imply

[tex] T \leq M?[/tex]
 

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Suppose it wasn't. Let epsilon be T-M (which is positive). What do you conclude?
 

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