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Jun
8
answered Why is one of the conditions of a vector space that if I add two vectors, the sum must be within the space?
Jun
8
answered What is the intuition and motivation behind a norm on a space?
Jun
8
answered How can I visualize the discrete metric?
Jun
6
comment Could we assign a numerical value to an infinitesimal?
all right then.
Jun
6
comment Could we assign a numerical value to an infinitesimal?
this isn't a definition. The first sentence is, at best, misleading, and I would venture to label it as wrong. Infinitesimals are not primarily (or at all) used to model objects so small that there is no way to them or measure them. The positive real numbers smaller than $2^{-2^{10^{100000000000}}}$ do that quite well.
Jun
6
comment Could we assign a numerical value to an infinitesimal?
can you please provide a reference to the definition you have in mind? As for engineers, they would not be able to do much of what they can do without analysis. Most of them though don't care about infinitesimals, since mainstream analysis uses the real numbers without any infinitesimals. There are authors though who claim, to various degrees, that a system with infinitesimals is better for engineering.
Jun
6
answered Could we assign a numerical value to an infinitesimal?
Jun
4
comment Local topological properties
won't help.....
Jun
4
comment Local topological properties
quite often your attempt will work, but you have to be careful. The example above shows you can't quite unify locality for all properties, so a single unified approach is hopeless. Having said that, it's typically quite easy to establish for any given local property if it's equivalent to having a basis with that property.
Jun
4
answered Local topological properties
Jun
3
comment Linear Algebra progression in our times
do you consider random matrices to belong to linear algebra?
Jun
3
comment Types, Sets and Categories
isn't it obvious from the length of my answer that it is indeed clear ? ;) My advise is intended with the best intentions.
Jun
2
comment Types, Sets and Categories
no, the objects in a category need not be sets. A category consists of a class (or a set) of objects, and for any two objects, a set of morphisms, or arrows, from the first object to the second. The objects themselves need not be sets. If you don't want to define categories in terms of sets, you can take an axiomatic approach, and formalize the axioms of a category. At this point though I'd say you are quite confused about what categories are and what they are good for. I suggest you read some more, and from different sources.
Jun
2
revised Groups of isometries
edited body
Jun
2
answered Types, Sets and Categories
Jun
2
revised Center of the categories $\mathbf{Grp}$ and $\mathbf{Ab}$.
edited body
Jun
2
awarded  Revival
May
30
answered Prove $KerT=KerS, ImT=ImS$, $T \ne S$
May
29
revised two notation: semi-metric and pesudometric
added 315 characters in body
May
28
comment n-globular sets and n-categories
Unless you are talking about strict $n$-categories, there are simply too many different definitions of $n$-categories for your question to make sense.