Hence one says "without loss of generality, A is at (0,0)" and so on. How might one automate this, in particular the detection that a "without loss of generality" argument is possible, or turn it into a procedure (and possibly even a formal proof)?
Now suppose is a point in ; without loss of generality we may take non-zero, and then we can normalise . Now one can think of as an inhomogeneous polynomial in just two variables , and by nondegeneracy we see that the gradient is non-zero whenever . By the (complexified) implicit fun...
There is a complementary approach, discussed for instance in this previous post, which is to spend the symmetry to place the variable “without loss of generality” in a “normal form”, “convenient coordinate system”, or a “good gauge”. Abstractly: suppose that there is some subset of...
the trained model is frozen and deployed. From then on, new incoming data is processed without any further adaptation or customization of the model. Soon, the model becomes outdated. In that case,
Not limited to a specific class; miscellaneous, concerned with all branches of a given subject or area. Broad (UK) A shallow lake, one of a number of bodies of water in eastern Norfolk and Suffolk. General A general fact or proposition; a generality. We have dealt with the generals; now...
What types of research should HVE colleges do? This article attempts to empirically study the second question while affirming the answer to the first question. HVE colleges focus on talent cultivation, which does not mean they will never engage in academic research. The key is to decide and ...
There is no loss of generality in assuming that x y 0 and that x is scaled to be of the form d.dd...d × 0. First, assume there is no carry out. Then the digits shifted off the end of y have a value less than -p + 1, and the sum is at least 1, so the relative ...
To know what you prefer, instead of humbly saying Amen to what the world tells you you ought to prefer, is to have kept your soul alive — RL Stevenson: a blog on books, films, art, music, culture
s going on there, there are all kinds of incentives to, so here are a couple of things to chew on: most of the Bitcoin mining that occurs happens in China (which means anyone who controls it ultimately controls the blockchain), and China already has more billionaires than the USA does....
Without loss of generality we may take to be odd, then . It is easy to see that is the only fixed point of , and so . An easy induction using (2) shows that where, for each , is the largest power of that divides In particular, as is odd, . Using the recursion we see ...