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"An infinite decimal expansion has the following meaning:

0.a1 a2 a3 a4... =

∞

∑ a

k=1

sup{∑ a

where ∑ is the sum from k=1 to k=n."

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Why is the second equality (about the supremum) true? (or why does it make sense?)

Thanks.

0.a1 a2 a3 a4... =

∞

∑ a

_{k}/ 10^{k}=k=1

sup{∑ a

_{k}/ 10^{k}: n E N}where ∑ is the sum from k=1 to k=n."

======================================

Why is the second equality (about the supremum) true? (or why does it make sense?)

Thanks.

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