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A mathematical object is an abstract object arising in philosophy of mathematics and mathematics. Abstract object: Abstract and concrete are classifications that denote whether a term describes an object with a physical referent or one with no physical referents. Denoting, specifying, describing an "object" (wasn't the abstract object the ...

Jul 14, 2014 · Wikipedia claims that "A number is a mathematical object used to count, label, and measure", but this definition fails to make sense after we extend $\mathbb{R}$. Does anyone know of any definition of number that can be generalised to complex numbers as well (and even higher order number systems like the quaternions)?

Aug 27, 2020 · (The definition of a function as domain X, codomain Y, and graph G can be found in Wikipedia's Function.) With dot notation, I would write: $(a,b)\in f.G \iff (b, a) \in f^{-1}.G$ Is there any precedent/examples for dot notation to "access" a "member" of an "object" in math? Is the idea of a mathematical object common?

Mar 15, 2022 · According to wikipedia a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. Is there any mathematical object which is hexahedral (like cubic) array of numbers?

Dec 9, 2024 · Such an f is called an isomorphism of the graphs G and G′. While the definition seems to consider the set of vertices instead of labels, I’m confused because many textbook and internet examples express graph isomorphism as a map from labels to labels just like the below picture from Wikipedia.

Jun 8, 2021 · Are truth values, true and false, specific mathematical objects, just like the number $5$ for example, so when someone says "logical truth", they refer to the specific mathematical object? In mathematical logic, yes, they are mathematical objects. And yes, 'True' and 'False' in this mathematical domain are just like the number $5$ in the domain ...

Aug 13, 2016 · There are quite a lot (I almost wrote "an infinite number") of different concepts that all use the word "infinity". Each does have a precise mathematical definition. They are not (ordinary real) numbers, though some can be called "numbers" in …

Mar 12, 2021 · A neat way to do this is to find the concept in English Wikipedia and then switch the language. So, let's find the German for the two uses of field. Here is the English article for field in the mathematical sense: Field (mathematics) and here is the German: Körper (Algebra). Now, let's find the day to day meaning of Körper (using Google ...

I was wondering whether there was any point to defining a mathematical object analogous to a unit vector without a well defined notion of addition and subtraction. $\endgroup$ – Alex Eftimiades Commented Jan 17, 2013 at 3:04

Sep 8, 2022 · An example which is still a good example: there's an object in mathematical physics called the 6-dimensional (2, 0) superconformal field theory, or "Theory X," which is predicted to exist because of string-theoretic arguments but has not been constructed at even a …