$(A)$ is arguably a lot stronger than $(B)$, or at least is, if relatively unrestricted. Such as a spin $1/2$ system in quantum mechanics, or a lexicographic entangled, system where its infinite in wrong sense, in the vertical, not in the horizontal, not within a basis of space/basis. Where the system is dense/or continuum dense/non-atomic/bottom-less in the wrong sense. Ie in a super-atomic or entangled lexicographic system. If its infinite /non-atomic in the wrong sense. Sometimes, even in a infinite and uniformly and non-atomic, continuous total order representation, nothing unique will come out. That is $F$ is a monotone strictly increasing function of some entity $x$ where $F(x)$ is the entity one wishes to order by $x$. Where in $(B)$ the numerical function, $F$ or representation is 'merely strong'. In contrast to $(B)$ a standard order embedding (strict monotone increasing function) (By cone, we mean that $\alpha K\equiv K$ for all $\alpha>0$ and by pointed, we mean that $K\cap-K=\ \, x=x_1 +x_2\, y=y_1+y_2 $$ Let $S$ be a vector space, and let $K\subset S$ be a closed, convex, and pointed cone with a non-empty interior. But given that the text deals with convex optimization, it was apparently considered helpful to refer to them as inequalities. And indeed, that's exactly what they are, and the book does refer to them that way as well. The book refers to these relations as generalized inequalities, but as Code-Guru rightly points out, they have been in use for some time to represent partial orderings. It is only when the quantities on the left- and right-hand sides are vectors, matrices, or other multi-dimensional objects that this notation is called for. It should be noted that the book does not use $\succeq$, $\preceq$, $\succ$, and $\prec$ with scalar inequalities for these, good old-fashioned inequality symbols suffice. I hope that I'm not being inappropriate by combining and expanding upon them here. There are packages that can be used, but more often using a carat and the \circ symbol.Both Chris Culter's and Code Guru's answers are good, and I've voted them both up.Upper case, such as upper case beta: \Beta.Lower case, such as lower case theta: \theta.Us \ln to typeset the natural log function.Īdditional symbols and commands for trigonometry Greek letters:.To write log base 7 of 5, we would write: Use an underscore to denote a different base. If you simply type log, this will be read as the variables l, o, and then g. Use \log to typeset the log function as a function.$\sqrt$ Special characters:Īdditional symbols and commands for college algebra Logarithms and exponential functions: We simply write:Ĭommands require one or more arguments after them, enclosed in curly braces. Symbols are standalone, and do not require an argument. Note: If you use these commands inside an equation editor (either the MathType editor itself or one in D2L), you do not need to use dollar signs. The equations can still be edited in the same way and converted back to MathType. But don’t panic, it will change “align” to “array” and be followed by a stated number of columns. Note: If you turn this into MathType and then back into LaTeX, it might turn it into an array environment, which requires a stated number of columns. If we wanted to show the steps to solving 5x plus 3 equals 13, we would type: Use double backslash (\\) to create a new line. Use the ampersand symbol to align each line. The Toggle Tex feature requires that this is itself placed inside dollar signs. To type a multiline expression in LaTeX, enclose it in an align environment. Without them, whatever you write is read as regular text. The dollar signs are key, as they distinguish a LaTeX math expression from regular text. For example, if we want to type 5x plus 3, we would type: To type a single line expression in LaTeX, enclose it in dollar signs. The commands are grouped by a general set of commands relevant to all courses. The list is not exhaustive, but covers most commands that a student would need for 100- and 200-level mathematics courses. Most of them can also be used in the learning management system D2L. This document focuses exclusively on LaTeX commands that can be used in Microsoft Word (with the Toggle TeX feature). PCC / Instructional Support / Creating Accessible Content / Math & Science / Essential LaTeX Commands for Mathematics Courses Scope and Purpose
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