John H
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 Oct11 comment Why are these logical statements not deemed to be equivalent? @ajotatxe Thanks for the comment. I'm inclined to agree, but I'd like some more feedback as the answer below has left me uncertain. Oct11 comment Why are these logical statements not deemed to be equivalent? Sorry for the delayed response, and thanks for getting back to me. The book is Core Maths for Advanced Level, which is basically covering the core sections of the UK maths curriculum that 16-18 year olds would study, so it's by no means a book on pure logic. Oct11 comment Why are these logical statements not deemed to be equivalent? I initially thought this, but it's only asking whether or not the point is on the line. It's not asking whether the equation the point was generated by is the same line. Oct11 awarded Student Oct11 asked Why are these logical statements not deemed to be equivalent? Sep25 awarded Commentator Sep25 accepted Without solving the equation, determine the nature of its roots: $x^2 + ax + a^2 = 0$ Sep25 comment Without solving the equation, determine the nature of its roots: $x^2 + ax + a^2 = 0$ @MickG Contacting the authors is a good idea actually. I hadn't considered that. There is no qualifier ruling that a is not equal to zero, so it's a definite problem. This book is 15 years old, but I've never been able to find any published errata for it. Sep25 comment Without solving the equation, determine the nature of its roots: $x^2 + ax + a^2 = 0$ Thanks for the confirmation. Sep25 comment Without solving the equation, determine the nature of its roots: $x^2 + ax + a^2 = 0$ @taninamdar Thank you. Sep25 asked Without solving the equation, determine the nature of its roots: $x^2 + ax + a^2 = 0$ Feb16 comment Active learning vs Passive learning in Math That actually makes sense, thanks. Feb16 comment Active learning vs Passive learning in Math Would you consider 'deliberate learning' to be the same as 'active learning'? Nov9 comment Logic - Translate a Math Statement Oh, now it makes sense. Thanks a lot! Nov9 comment Logic - Translate a Math Statement Doesn't "you must pay the daily fee unless you are a subscriber to the service" imply they are mutually exclusive, rather than inclusive? Jul23 awarded Scholar Jul23 accepted Why can/do we multiply all terms of a divisor with polynomial long division? Jul23 comment Why can/do we multiply all terms of a divisor with polynomial long division? Ah, now that makes complete sense. I think that was probably what I couldn't understand all along. I went back over the 48 / 28 problem and realised that I'd get 1 + (20 / 28). Writing that as (4 * 10 + 8) / (2 * 10 + 8) gives 2 - (8 / 28). Then I realised they are the same answer, expressed differently. I can't thank you enough for your help. Jul22 comment Why can/do we multiply all terms of a divisor with polynomial long division? Thank you, too, for your answer and again, I'm sorry it's taken such a long time for me to reply. I like that you've given me a completely different way to view the problem. Jul22 comment Why can/do we multiply all terms of a divisor with polynomial long division? I can see that it rebalances, but I'd like to understand how someone developed this method, assuming this was created for real numbers first, and realising it would work like this algebraically. The result is the same but the rebalancing by having a negative remainder seems very different to the method for real numbers (at least to me).