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We know that the measure of an uncountable set might be zero for instance the famous Ternary Cantor set. But sometimes it might as obvious. Today I was thinking about some problem and the following question just popped in my mind:
Let $E$ be the set of real numbers in the open interval $[0,1]$ whose decimal representation does not contain the digit 8 anywhere.What is the measure of E?
All I can prove about $E$ is that it is uncountable?Could somebody kindly help me?I would be most obliged for nay hints/insights/responces

Asaf Karagila
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AgnostMystic
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  • Hint: The ternary cantor set is the set of all real numbers in $[0,1]$ whose ternary representation does not contain the digit $1$. – Zim May 13 '22 at 13:46
  • @lulu ,thank you for sharing .Every time I pose some really nontrivial exercise or problem myself ,I think I must be the first person to pose it just because of the sponatnaeity and bizarreness. But these math guys have almost thought about anything that ordinary people like me can think.Anyways ,still glad to learn new bits of maths – AgnostMystic May 13 '22 at 13:55
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    @AgnostMystic It is distressingly difficult to come up with a truly new question. – lulu May 13 '22 at 13:58
  • indeed @lulu.But I think we should all follow in the footsteps of the great Erdos here.Problem posing is as important as important as problem solving – AgnostMystic May 13 '22 at 14:04

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