After four days...

When I first saw this, knowing that I had forgotten what I'd once read about how to compute square roots with an algorithm, my initial reaction was to use linear approximation, but soon realised that you specifically asked for an algebraic technique.

I'll admit it, I couldn't find a way, yet I didn't want to give up and look up on Google. Instead, I laid the problem to rest first, and continued with learning Series.

Then, it dawned on me that I could approximate the value of √7 using Binomial Series.

√7 = √(4+3) = √[4(1+0.75)] = 2[(1+0.75)]^(1/2) ≈ approximate value if enough terms are computed using Binomial Series.

Then I realised that ancient Babylonians didn't know Binomial Series.

That's as far as I can go. Anyway, I can finally utilise the importance of your past Maths tutorial pdfs.

There's a mathematical proof of it, why should one not want to believe? It's like asking someone whether he/she believes in the Pythagoras's Theorem or not.

His theory on infinity was shunned initially, but all mathematicians acknowledge it now.

Edit: I have read up, and it was interesting.

This post has been edited by maximR: Oct 23 2014, 11:58 PM

I watched this when it was first uploaded, as well as a host of other videos about Cantor's Set Theory, by universities like Yale. Hence, my 'biased' view that it's absolute, like the fact that there are an infinite number of primes, which is indisputable.

Further, her question asks about whether we believe it or not, which is a tough question, because one can either take the proofs for granted and then say with certainty that there are different magnitudes of infinity, or one can choose not to believe, but if a person doesn't believe in Cantor's theory without any sound reason ( e.g. has sound arguments against the theory backed with strong mathematical intuition and prior knowledge ), it'll be a judgement based on ignorance.

For example, when someone asks whether I believe in Einstein's General Theory of Relativity or not, I will, without a second of doubt, say yes, but bear in mind my mathematical capabilities are nowhere near the standard requirement to even begin studying his theory. But if I were to say no, I'd be very, very silly because on what basis do I base my stance upon? Sure, there may be debates about his theory being incomplete, but that doesn't mean I can safely discount the theory just because I've read or heard a few arguments against it. On the contrary, there are numerous experiments which have supported his theory.

This post has been edited by maximR: Oct 24 2014, 01:51 PM

Where and what are you studying right now?

How did your PhD go?

You can do this without induction, by using contradiction and Factor Theorem. Anyway, are you doing this for your degree?

I hope you can, so you'll be here to share the beauty of Maths!

The coffee wants to remain in its original position, but you move forwards with the cup. The coffee has nowhere to go, it overflows.

It's somewhat like a pendulum in a car moving backwards as the car accelerates forwards.

Where are all the Maths/Physics enthusiasts?

Then I might be reviving it every now and then since I have more time now.

Anyway, I'm interested in the courses you took as an undergrad, specifically, what classes you took in your first, second, and third year respectively. How did you cope with the classes, and which one of those did you find particularly difficult? What books helped you the most?

I'm looking at Real Analysis and I realise that there are a lot of ground (logic, set theory, functions) to cover if I were to have a meaningful exploration of the subject.

Switched to Pure Mathematics?

I'm still in the process of completing my A-Levels. It's a complete waste of time. I'm not waiting for university to learn, so I've been reading and thinking about Maths.

Throwing around fancy words doesn't make one smart! You can always learn these things if you want to. What is your background?

There are more problems. One of them, a topological problem, was solved by a mathematician who declined the Field's Medal.

How is everyone doing? I've been noticing a lot of 'homework' problems lately, and they are all applied maths problems. Nobody doing pure mathematics?

Huh? That's one of the weirdest requirements I've seen -- two science subjects as a prerequisite for a pure mathematics program!?