Can't solve any problems: After finishing chapter in Herstein's "Topics in Algebra", I've been trying to solve problems for several weeks.

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Boi

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After finishing a chapter from my math book, I've been trying to solve problems listed after it for several weeks. I am lost and I have no clue how to even approach most of them. Should I persist or give up and move on to the next chapter?
 
Boi said:
After finishing a chapter from my math book, I've been trying to solve problems listed after it for several weeks. I am lost and I have no clue how to even approach most of them. Should I persist or give up and move on to the next chapter?
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No. Some chapters may contain information that you won't need later, but usually the next will assume you've mastered this material.

Tell us what the chapter taught, and show us a problem or two, with your attempt (or what stops you from trying. Hopefully, we can try to find what you've missed.
 
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Thank you for your advice!
The chapter is from Herstein's "Topics in algebra". It teaches about mappings from sets to sets. The problem I struggle with is this:
"If [imath]S[/imath] is any set, prove that it is impossible to find a mapping of [imath]S[/imath] onto [imath]\mathcal{P}(S)[/imath]"
Here, [imath]\mathcal{P}(S)[/imath] means the set of all subsets of [imath]S[/imath]. I find so hard because [imath]S[/imath] may be infinite. I attempted it, but all of my attempts didn't have "purpose" (i don't know a better word for this). They were all like this: "If i do X, then maybe it will somehow solve the problem". Random shots, basically.
 
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Boi said:
Thank you for your advice!
The chapter is from Herstein's "Topics in algebra". It teaches about mappings from sets to sets. The problem I struggle with is this:
"If [imath]S[/imath] is any set, prove that it is impossible to find a mapping of [imath]S[/imath] onto [imath]\mathcal{P}(S)[/imath]"
Here, [imath]\mathcal{P}(S)[/imath] means the set of all subsets of [imath]S[/imath]. I find so hard because [imath]S[/imath] may be infinite. I attempted it, but all of my attempts didn't have "purpose" (i don't know a better word for this). They were all like this: "If i do X, then maybe it will somehow solve the problem". Random shots, basically.
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This sounds like a difficult, albeit a well known, problem, unless there was something in the chapter to lead you to the proof. You might find this page informative: https://en.wikipedia.org/wiki/Power_set#Properties
 
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