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Huh?

Yep, of course the formal proof would proceed by something like induction, using that multiplication of reals is associative. Such a proof is terribly boring though and doesn't tell you anything that is at all surprising. Note though, that even this formal proof would only show that...

Hopefully analysis appears more attractive to you than stats after it!

+1 that site was very useful in the past.

I'd say linear algebra and calculus are the two main general things you have courses in in first year. The former is (in first year) a pretty dry computational subject. If you eventually wanted to learn linear algebra properly and are willing to put some hard work in I would recommend Halmos-...

Cool, enjoy it! I wish I had a book that good to learn analysis from the first time.

How much / from where? Big Rudin occupies a prominent spot in my office collection.

Yeah, if you ever learn any complex analysis or analytic number theory your mind will be blown. Staggeringly beautiful subject.

Multiply by 1 + cos(x) on numerator and denom, and use that sin(x)/x -> 1 as x -> 0. Or use cos(x) = 1 - 2sin(x/2)^2.

+1 for Baby Rudin for a first course in analysis. And Herstein's Topics in Algebra would be excellent as an accompaniment to second year algebra.

Firstly, you shouldn't expect too much rigour in high school. Constructing the complex numbers is a little more subtle than just saying: "Let's assume that there exists a square root of -1 and call it i." In this case, the flaw is that sqrt(ab) is not necessarily equal to sqrt(a)sqrt(b) for...

Well they wouldn't be called "complex numbers" anymore. Yep, depending on what you do, you might.

No, not when i means what it normally does.

The proof means that 1 has no non-real complex square roots. Similarly we can show that 1 has no non-real quaternion square roots. If we take the word "extended number" to loosely mean any extension of the complex numbers which still obeys all the nice properties of the real and complex numbers...

1. Yeah, shift alpha by pi to get between a negative and positive R. Everything will work out the same of course. Formulae just look nicer with the convention of taking R > 0 I guess. 2. Within MX2 methods, you can use the perpendicular distance formula to find the volume of the infinitesimal...

Really? How do you know this?

I have my own views on the matter which would have come up elsewhere on bos before, but I would be interested in hearing the thoughts of the mixture of (mostly) HS students, HS teachers, and undergraduates who frequent this site (without any bias from reading what I have to say first). Some...

Re: HSC 2013 4U Marathon haha obviously a counter-troll.

Re: HSC 2013 4U Marathon "Positive integer solutions" means a,b,c must be positive integers. You have not restricted n though beyond saying that it is larger than 2. So a=b=3, c=4 solves the equation with n=log(1/2)/log(3/4). Hence the claim is untrue.

Yep sure.