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i read in Spivak that for every upper bounded non empty sets A and B,

sup(A+B)=sup(A)+sup(B). but later he wrote other prove which claim that

for every function f and g in a close interval exist sup(f+g)<=sup(f)+sup(g)

and not necessarily sup(f+g)<=sup(f)+sup(g). how does it make sense?

Thanks

Omri

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# Least upper bpunds

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