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 Sep22 comment Statements in Euclidean geometry that appear to be true but aren't Uhm... isn't this one true? Sep22 comment How to divide currency? Suppose you only have 2 and 3 cent coins, then you can have 1 cent net exchanges. Sep22 comment How to divide currency? I don't think this is a very mathematical or enriching answer. Sep22 comment What are imaginary numbers? @MakotoKato: I agree with you insofar that the idea of atoms is very real, and it very neatly describes the small thingies we're seeing through a microscope. I feel you are also completely missing my point, however. Sep21 comment What are imaginary numbers? @MakotoKato: If "to exist" is defined in the sense that you can see or feel it, yes, but feel free to propose a clear definition of existence. However, my point is that imaginary numbers are just an idea, just like stories and limited liability companies, and in that sense they are just as "real" as integers. Sep21 comment What are imaginary numbers? @MakotoKato: Schroedinger's equation does not exist in the physical sense, it's just an idea which apparently is very applicable to the measurable world. Sep20 comment What are imaginary numbers? @MJD: this is exactly the confusion many people have with numbers, and which I am trying to point out, but it may be obvious that there is no way to measure love in the way you measure an electric potential. However, the /explanation/ of love is a very helpful one. Sep20 comment Studying mathematics efficiently @Graphth: SOME humans learn about 70% of what they learn by doing, yes, but it is a rather short-sighted statement to say that this is true in general. Sep20 comment Studying mathematics efficiently This is very much an example of what Matt said. I personally do not benefit from exercises at all - I either get the material or I don't. If I don't get it, I am helped by more theory and examples, but exercises hardly ever help me. Sep20 comment What are imaginary numbers? Real numbers don't "exist" either, they're all just mathematicians' ideas. Sep20 awarded Enthusiast Sep18 comment Example where $f\circ g$ is bijective, but neither $f$ nor $g$ is bijective Interestingly, your functions are bijections, but on different domains and codomains. Sep17 comment Advice for choosing an MSc or PhD. If I get your answer correctly, a MMath is "lower" than a MSc, is that right? Then what is the difference between a MMath from Warwick and a MMath from Cambridge? Sep17 comment Prove that every open set in $\mathbb{R}$ is a disjoint union of open intervals you are right, I was confused by Clive's answer :) Sep17 comment Prove that every open set in $\mathbb{R}$ is a disjoint union of open intervals 3. prove that this gives you a countable set of classes Sep12 comment How many subsets are there in a set of size $n$? No combinatorics Try induction, perhaps. Sep4 answered how to be good at proving? Sep3 comment Method of Least Squares-Why is it preferred? Mathematically, an error is defined as the absolute value of the difference, and errors never cancel out. Sep3 comment Method of Least Squares-Why is it preferred? Please define "negative error", and in any case, clarify your question. Sep3 comment Method of Least Squares-Why is it preferred? This answer does not explain why the method of least squares is as popular as it is.