# user18921

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 Mar3 comment Categorical foundations without set theory @TomLeinster, consider an infinite page that begins with a finite set of strings written on it. There are rules that allow you to write more strings on the page, given that certain other strings are already written down. Then we can think of the set of all strings writable on the page as a (perhaps infinite) set. But in reality, at any one moment in time, there are only finitely many strings written down. Hence the aforementioned system (consisting of the paper and its rules) could be described as a potentially infinite set. Mar1 comment What are the worst notations, in your opinion ? I think this is a great question; because, if you're writing mathematics in notation the reader does not feel comfortable with (or refuses to feel comfortable with), you're probably not doing a very hot job of teaching/communicating. So, it would be useful to know what people are/aren't comfortable with. Feb11 accepted Semitransitive relations Feb10 asked Semitransitive relations Feb3 accepted What do we call a set that has one or fewer elements? Jan7 comment Axiomatic definition of integers Are you sure that every commutative operation is also symmetric? I think this is unprovable without some further assumptions. Nov6 comment What is the standard notation for group action How about $X \in \mathrm{Set}^G,$ where $G$ is viewed as a category with one object. You can write $x \in X$ to mean that $x$ is an element of the unique object in the image of $X,$ and you can write $g \in G$ to mean that $g$ is an arrow of $G$. Finally, $gx$ can be defined as shorthand for $(X(g))(x).$ Sep24 comment Is there a (standard) name for $\bar{A}\setminus A$? I don't think this is good terminology, because the intersection of the exterior of a set with its boundary will always be empty, and therefore needn't equal its external boundary. However the basic idea of modifying the word "boundary" with an adjective is a good one, in my opinion. Sep21 awarded Popular Question Sep13 accepted Dealing with undefined expressions in predicate logic Nov19 revised Set Exponentiation: Is Y always disjoint from Y^X? added 2 characters in body Nov17 awarded Self-Learner Nov17 awarded Teacher Nov17 answered Set Exponentiation: Is Y always disjoint from Y^X? Nov17 comment Set Exponentiation: Is Y always disjoint from Y^X? quid, I think you might be right. Is there any way of migrating the question? Nov17 comment Set Exponentiation: Is Y always disjoint from Y^X? For instance, if $f$ and $g$ are functions that returns sets, we cannot overload the union operator by writing $(f \cup g)(x) = f(x) \cup g(x)$. That's because $f$ and $g$ are sets, and so $f \cup g$ already means union of the sets $f$ and $g$. We cannot just simply endow it with a second meaning, as this would be ambiguous. Nov17 comment Set Exponentiation: Is Y always disjoint from Y^X? So to summarize the problem. Suppose we redefine $3$ as you're suggesting, or even better let 3' be the constant function that returns 3. We can invent a new plus symbol that applies to functions, as in $f \oplus g$. So then we can write $(3' \oplus f)(x)=3'(x)+f(x)=3+f(x)$. Now what we'd really like is to simply be able to overload the $+$ operation. So $(3'+f)(x)=3+f(x)$. However, we need $\oplus$ to have a domain that is disjoint from the original operation $+$ before we can overload $+$. This motivates the question asked. Nov17 awarded Commentator Nov17 comment Set Exponentiation: Is Y always disjoint from Y^X? Suppose I want to write $3+g$ in order to mean the map $x \mapsto 3+g(x)$. Are you suggesting that the best solution is to redefine $3$ so that it's the constant map? Nov17 asked Set Exponentiation: Is Y always disjoint from Y^X?