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A statement such as $a>b<c$ could be useful if $a$ and $c$ are not contestants. I would interpret it as $a>b\ \mathrm{and}\ b<c$, i.e. $b<\min(a, c)$. In general, I'd interpret a statement of the form $a★b‡c$ as $a★b\ \mathrm{and}\ b‡c$. I'm pretty sure this is also how Python does it, for example.


"By default", all chained inequalities can be considered as illegal, because from an computer scientist's point of view and assuming that $<$ is left-associative: $a<b<c$ simplifies to $\text{\{True or False\}} < c$ which does not make sense ("type error"). To get around this, one defines the allowed combinations and their "expanded forms" as ...


In class I define the matrix product by $(AB)_{ij} = \sum_{k = 1}^{q}A_{ik}B_{kj}$ where $A$ is $p \times q$ and $B$ is $q \times r$. In my experience what causes the most confusion is not the subscripts indicating the component, but the meaning of the summation notation. Students do not identify the written formula with $(AB)_{ij} = A_{i1}B_{1j} +A_{i2}B_{...


As you realize, this In my brief experience, I’m finding that my written diagrams or notations are not ideal. Admittedly, I will draw operators, numerals, and arrows on-the-fly, and they don’t always clearly communicate the process, especially when looking at them a few days later. is part of your problem. I suspect you may have difficulty ...

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