Exercise · ZW-CANTOR-S-DIAGONAL-THEOREM-005 · ★★☆ Intermediate

With \(s_1=000\ldots\), \(s_2=111\ldots\) and \(s_3=0101\ldots\), what are the first three terms of the diagonal sequence \(t\), where \(t(n)=1-s_n(n)\)?

Choose one option.

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  • D. \(1,0,1\)

Explanation

\(t(1)=1-s_1(1)=1\), \(t(2)=1-s_2(2)=0\) and \(t(3)=1-s_3(3)=1\). The other sequences do not flip each diagonal term.

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Review the concept: Cantor's diagonal theorem

Theorem proving that the set \(\{0,1\}^{\mathbb{N}}\) of binary sequences is not countable, by building a sequence that appears in no list.

\[t(n)=1-s_n(n)\]

More practice problems: cantor's diagonal theorem

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