Question

Prove the following assertion and show as much detail as possible to justify your answer.

{eq}displaystyle L=0^n1^m,quad ngeq 1000,quad mleq 500

{/eq}

EXPERT ANSWER

To prove the given expression

{eq}L= 0^{n}1^{m}, ngeq 1000 , mleq 500

{/eq}

{eq}{n_{1}=1001 , n_{2}=1002 , n_{3}=1003… text{so on (to the infinity)}}\

n^{1001}=0 \

n^{1002}=0\

n^{1003}=0\

\

\

text{and so on(to the infinity)}

{/eq}

{eq}text{and}\

\

text{taking}\

1^{0}=1\

1^{1}=1\

1^{2}=1\

…\

…\

text{and so on(to the infinity)}

\

text{any power of 1 remains the 1}

{/eq}

{eq}text{finally}\

text{L=0*1}\

text{L=0}\

{/eq}

therefore,

{eq}L=0^{n}*1^{m}=0\

{/eq}

hence proved

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