Well, I feel it has to be, because what other definition do you propose that's more trivial to understand?
Thanks, RuiAce, but I didn't mean to imply it was not the optimal definition, but I think the concept of less than is probably granted intuitive as people tend to be taught the ordering of numbers, first, or develop a slightly hand-wavy definition of 'larger and smaller'. Meanwhile, mathematics can be more strictly viewed through a definition such as the above, which then lends to the creation of 'ordering', so to speak. Alternatively, one could view it as the difference between the two numbers, p ≠ 0, and in the set of natural numbers, but obviously, the two definitions are equivalent.
Wednesday 27thHi,
I again made some progress through
Physics, in the
Motion in a Plane chapter, primarily learning about centripetal acceleration, and learning a couple of derivations of a = v^2/r, as well as the unit vectors of polar coordinates, u_r and u_θ, and completing a large quantity of the associated problems. I am now ready to start
Particle Dynamics, a chapter that introduces concepts such as mass, weight and force in general. Although I have already learned much of this material, mostly kinematics, through Khan Academy and other resources, I will be venturing onto completely new topics, primarily with a calculus approach, perhaps mid-August, or a couple of weeks from now.
I worked on some art, for some period of time, and my skills are improving in this time-frame. I tend to warm-up with a few relatively easy tasks, such as drawing a still-life from a real scene, but then attempting to draw dream-scenes, that of which are of particular interest to me. My blog, which I seriously started this month, has enjoyed a 10x jump in traffic today, a brilliant contrast to the modest goals I was setting the night before, possibly as a result of using Stumbleupon/Mix, and one particular post really resonated with my audience, earning at least 30 additions to other people's collections.
Languages are going well; I found a comprehensive course on Memrise , whilst not too difficult, supposedly gets harder, and starts from around B2 level,
my current level. One advantage is that it isn't clouded with phrases that while useful and eloquent on occasions, have very limited usage, unlike a single word, such as
hebdomadaire, or weekly. Meanwhile, Russian is taking shape, as I am starting to learn more nouns, such as девушка and мальчик, as I seem to have exhausted the primary prepositions and conjunctions. As I am nearing the end of CLC Book 1 for Latin, I am considering requesting my Latin teacher to receive Book 2, but I am not sure of his reaction, as I have so far made an appearance of fading into the background, as some sort of experiment and exercise in self-control. So far it seems to have worked, but nothing serious has actually happened, with the class barely commencing simplistic translation of three word sentences. I just don't want to be accused of arrogance, and of 'upsetting' other people.
My musical studies have gone well, and I have now learned the first 6 Hanon and Popper studies, and will spend the next couple of days revising 3, 4, 5 and 6. The school is offering a couple of masterclasses with Melbourne Conservatorium, but given there are only 2 places per school, and the reality that I have finally gone no-contact with the Music School, having put up with over 3 years of their hatred and jealousy.
History is going well, with my essay practically complete and Herodotus being a rich and interesting resource. Meanwhile, I have been putting off study of the set book for English, instead opting to improve my writing ability in my English study period through a mix of creative, persuasive, and informative texts, and doing some analyses of well-known and essential pieces of literature, and I am now about to commence
Wuthering Heights, by Emily Bronté
Bye for now, and comments are always welcome.