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I recently just realized that "sure" and "of course" are different in #English in a daily conversation. My friend said, "You going home?" I mindlessly replied, "Sure." Then I just thought, oh I should've said "of course" instead. It feels so strange: I was taught in school that "sure" and "of course" are the same, and no one told me otherwise, but I just knew it without even knowing I knew it -- it was after I misused the phrase myself once that I realized I knew it.
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break,next, andredoin Ruby
Many languages support breaking out of nested loops, such as Perl, Java, JavaScript, C#, etc. Languages that have gotocan also do this easily. However, in most other languages, it is not easy to break out of nested loops. I want to introduce a way to do this in Ruby. -
Free trade (single good case)
I set up a simple model to determine the production and consumption in free trade between nations. -
A measure-theoretic formulation of statistical ensembles (part 2)
For sake of rigor and generalizability, I feel it necessary to try to have a mathematical formulation for statistical ensembles. I chose measure spaces as the underlying mathematical structure of thermal systems and tried to justify the method of statistical ensembles by deducing them from some axioms. -
Summarizing my methods for studying
I summarized my methods for studying. This can be served as a guide for those who have started learning math and science. -
A measure-theoretic formulation of statistical ensembles (part 1)
For sake of rigor and generalizability, I feel it necessary to try to have a mathematical formulation for statistical ensembles. I chose measure spaces as the underlying mathematical structure of thermal systems and tried to justify the method of statistical ensembles by deducing them from some axioms. -
The core of a voting system is the intersection of Pareto sets
There is a very neat relation between the core (the set of proposals that defeats every proposal) of a voting system and the Pareto sets of the voters. Suppose there is a voting system of quota , then the core is the intersection of all such sets: the Pareto set of of the voters. -
Relationship between the Gini coefficient and the variance
Both the Gini coefficient and the variance are measures of statistical dispersion. We are then motivated to find the relationship between them. It turns out that there is a neat mathematical relationship between them. -
Distinguishing all the letters in handwritten math/physics notes
Personally, I have the demand of handwriting math/physics notes, but an annoying fact about this is that I usually cannot distinguish every letter that may be possibly used well enough. In this article, I will try to settle this problem. -
手纸本
何为手纸本? -
Introducing bra–ket notation to math learners
Bra–ket notation is a good-looking notation! I am sad that it is not generally taught in math courses. Let me introduce it to you.
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