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Aug
13
asked Question about continuous functions and indefinite integrals
Jan
14
comment The accumulation points for Dirichlet's function
Yes, I think you're right. I'm relatively new to Real Analysis, and english is not my native language (the books are not in english) so sometimes the terms get jumbled up.
Jan
14
comment The accumulation points for Dirichlet's function
Accumulation point, apparently in English they're also called limit points.
Jan
14
comment The accumulation points for Dirichlet's function
Yes, here it is link
Jan
14
revised The accumulation points for Dirichlet's function
added 170 characters in body
Jan
14
asked The accumulation points for Dirichlet's function
Jan
12
awarded  Commentator
Jan
12
comment I want to study mathematics ahead of high school, but I found that I'm rusty on the elementary stuff
Yea, sorry, English is not my first language. What I meant to say is that "For me, personally, they're a bit too slow-paced".
Jan
11
accepted I want to study mathematics ahead of high school, but I found that I'm rusty on the elementary stuff
Jan
11
comment Is this proof about $a^3>a \rightarrow a^5>a $ correct?
Yes, you are right. Now that I think of it, it implies that a is different than 0 and $a > -1$.
Jan
11
comment Is this proof about $a^3>a \rightarrow a^5>a $ correct?
Well, when $a = 0$ then simply everything is 0. 0 at any power except 0 is 0. But I don't think that's what they had in mind when they made the exercise and put it in the textbook.
Jan
11
comment I want to study mathematics ahead of high school, but I found that I'm rusty on the elementary stuff
Thanks for the recommendation. As for spending, anything within reason is OK. I could afford, maybe 3 or 4 textbooks like that. Also, free resources are more than welcomed (but from personal experience, good ones are hard as hell to find). In fact, that book looks more or less like what I'm looking for. I'll find a way (maybe look over the old notebooks) to get a proper grip on 5th - 8th algebra, and paired with that book I should be set (it seems to have sequences, trig, functions and the works). And it's for the International Baccalaureate ? Even better then.
Jan
11
comment Is this proof about $a^3>a \rightarrow a^5>a $ correct?
It doesn't even hold for negative a. If we take -2, we get $-8 > -2$ which is obviously false. That's because you're dealing with odd powers (where the sign counts). So, his proof is correct and the fact that $a^3 > a^1$ sort of implies you're dealing with $a \in \mathbb{R}_+$.
Jan
11
comment I want to study mathematics ahead of high school, but I found that I'm rusty on the elementary stuff
The teacher (though I'm not sure of how much to rely on his opinion) said that it's no good, because it's really old, and it's been modified over time in order to match the new curriculum, and now it's a potpourri of stuff, not very useful for learning. From what I've seen, it's quite comprehensive on the theoretical side, but offers almost no exercises and no indication on how to do them. And, even it were good it only covers 9th grade. I need a recap on older stuff, and I also need more advance stuff (trig, and other analysis pre-reqs). Thanks for taking the time to answer.
Jan
11
awarded  Teacher
Jan
11
answered Is this proof about $a^3>a \rightarrow a^5>a $ correct?
Jan
11
awarded  Supporter
Jan
11
comment I want to study mathematics ahead of high school, but I found that I'm rusty on the elementary stuff
Thanks for the reply, but I have tried learning from KhanAcademy and I can't. It's just not my style. Either having someone explain it to me face-to-face or using a book, because it's either a faster pace or -in the case of a book- I can set my own pace. However, I could learn the stuff from some other source, ideally written, then do the practice there and maybe even use it as a list of things to go through. So, thanks for the suggestion.
Jan
11
asked I want to study mathematics ahead of high school, but I found that I'm rusty on the elementary stuff
Jan
10
awarded  Scholar