this post was submitted on 14 May 2025
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submitted 2 weeks ago* (last edited 2 weeks ago) by h3mlocke@lemm.ee to c/math@lemmy.ml
 

Part (b). So, this is from the introduction of a discreet math book, How to Prove it, idk where to even start with this, and figure that since it's part of the 1st question in the intro that I should know how to do it. But, alas.

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[โ€“] h3mlocke@lemm.ee 2 points 2 weeks ago (1 children)

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Thanks so much, that was super helpful!

[โ€“] cosecantphi@hexbear.net 2 points 2 weeks ago (1 children)

You're very welcome! I'm slowly teaching myself what is essentially a mathematics undergrad degree, and I'm familiar with the book you're using, so if you ever have any other questions feel free to ask!

Word of advice: In most math books, especially at lower levels, the majority of the exercises will nearly always be some sort of direct application of the theorems and proofs in the preceding chapter of instruction.

So when you feel stuck, you should go back to those theorems and try to make sure you really understand what the proof is saying. Like try to be skeptical about the statements and examine them until you are fully convinced that the proof is ironclad. Then it'll be much easier to spot which theorems each exercise is meant to provide elaboration/nuance on, especially the earlier exercises in a chapter.

The later exercises in a chapter tend to be much more difficult, but you'll nearly always be able to prove them with the theorems you've already learned, it's just that the harder ones will be essentially foreshadowing theorems in future chapters. So the longer you stick with this, deeply examining every theorem and attempting every exercise, the easier it becomes as you begin to understand the pedagogical intent of the author.

[โ€“] h3mlocke@lemm.ee 2 points 2 weeks ago

Thanks so much! I will probably post more problems. I went back to school a few years ago and this was my next math class so I wanna work through it and think about maybe finishing my math BA, but also might just keep doing math for fun. ๐Ÿคทโ€โ™€๏ธ