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I'm self studying Baby Rudin and trying to do exercises, i got stuck at exercise 2.18 then looked up the answer from solution manual but the proof includes so much algebra for me to understand where these variables came from and why it is written this way. How can i improve myself for easily seeing the reasoning at this kinds of proofs? This exercise is just an example for kinds of proofs i am having trouble. enter image description here

Ali
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    It's hard work! You have to trust that it will get easier with practice and experience. One way you might have come up with an idea like this is by knowing that the Cantor set is perfect and asking if the construction of the Cantor set can be modified to exclude $\Bbb Q$. This proof is quite opaquely explained - I would personally at least include a sentence like JDH's summary here. (Personally, my first thought looking at this qn is "I wonder if you can just translate the Cantor set so it doesn't contain any rationals", and indeed you can...) – Izaak van Dongen Nov 16 '23 at 14:15
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    I strongly suggest you read this handout: https://math4cs.com/23fa/documents/pudding.pdf – ElectricShadow Nov 24 '23 at 23:19

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