Benjamin Braun
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Registered User
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Jan 29 |
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Which popular games are the most mathematical? Set is usually a hit at parties (coming from an undergraduate at a school that ranks in the top party schools in the US.) |
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Jan 29 |
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What kinds of operations are well-defined when working with sets, classes, conglomerates, and yet higher order collections? @David - TG (based on ZFC) is a material set theory, so I have the pairing operator at my disposal (I think?) |
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Jan 28 |
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What kinds of operations are well-defined when working with sets, classes, conglomerates, and yet higher order collections? @Zhen - Yup! I've looked into the Tarski–Grothendieck set theory, which makes working with sets and classes intuitive. It doesn't seem like it provides these tools for conglomerates and higher-order collections, but it's not like I needed that anyway for category theory. |
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Jan 28 |
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What kinds of operations are well-defined when working with sets, classes, conglomerates, and yet higher order collections? Zhen, in regards to (2), if I have two mathematical objects $A$ and $B$, and I throw them into a set, how was I to know that $A$ and $B$ were not classes? Or is this simply my intuition being at odds with the mathematical formalism? |
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Jan 28 |
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What kinds of operations are well-defined when working with sets, classes, conglomerates, and yet higher order collections? added 4 characters in body; edited title |
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Jan 28 |
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What kinds of operations are well-defined when working with sets, classes, conglomerates, and yet higher order collections? Whoops, you're right. It's probably too late for me to be asking this. Editing question to clarify that by "axiomatic" i mean "implied by the axioms" |
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Jan 28 |
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What kinds of operations are well-defined when working with sets, classes, conglomerates, and yet higher order collections? added 149 characters in body |
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Jan 28 |
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What kinds of operations are well-defined when working with sets, classes, conglomerates, and yet higher order collections? Yes, editing question to clarify that I'm interested in the more modern theories, NBG and SEAR, etc, which were developed (as far as I can tell) to provide better support for classes and higher order collections. |
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Jan 28 |
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What kinds of operations are well-defined when working with sets, classes, conglomerates, and yet higher order collections? added 78 characters in body |
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Jan 28 |
asked | What kinds of operations are well-defined when working with sets, classes, conglomerates, and yet higher order collections? |
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Jan 26 |
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What is the difference between a function and a morphism? @Feldmann - No, I wanted the domain of $f$ to be the set containing $A$, simply because $A$ may not be a set, and the domain of a function is a set by definition. |
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Jan 26 |
awarded | ● Scholar |
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Jan 26 |
awarded | ● Supporter |
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Jan 26 |
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What is the difference between a function and a morphism? Got it. I've resolved my issue by thinking of morphisms as just triples of the form $(x,y,z)$ where $x$ and $z$ are objects of the category and $y$ is some mathematical object. So in your example, $f$ would be $(A,u,B)$ where $g$ would be $(A,v,B)$ where $u$ and $v$ are what is making $f$ different from $g$. |
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Jan 26 |
asked | What is the difference between a function and a morphism? |
