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1d
answered Geometric Morphism
1d
answered Is an “$\aleph_0$-limit” a finite limit or a small limit?
Apr
26
comment Deducing the existence of particular functions $\mathbb{N}\longrightarrow\mathbb{Q}$ in the context of Tom Leinster's “Rethinking Set Theory”
I guess Eric wanted to head you for restating your condition about 'given $r_1,r_2,\dots$ rational numbers' in a form that is rigorously expressible in this theory. And, I guess, what you will find is that this '$r_1,r_2,\dots$' is a priori given by a function $\Bbb N\to\Bbb Q$.
Apr
26
comment Difficulty finding a power series representation
Well, yes it should be something like that.
Apr
26
comment Where does the gap come from?
Or, watch carefully the points $(5,2)$ and $(8,3)$ on both pictures.
Apr
24
answered Difficulty finding a power series representation
Apr
24
answered Diagonalization of Linear Transformations
Apr
24
answered What exactly is a p'-group?
Apr
24
comment Sets vs Objects, is there a difference
Well, you can create a new instance to an already defined class, and the class stays the same, while if you add a new element to a set, you're going to get a different set.
Apr
24
comment Extension Operator.
What about the following closure operator on the class of (isomorphic types of) your modules? Let a subclass $U$ be closed if $A,B\in U$, $0\to A\to C\to B\to 0$ (ex)$\,$ implies $C\in U$.
Apr
23
comment Cross product angle formula
No, "in general", for all $\theta$ the formula you asked is false, except for $\theta=k\pi$ whence your formula happens to be valid.
Apr
23
revised Cross product angle formula
added 28 characters in body
Apr
23
comment Cross product angle formula
It's simply because, by coordinates, the dot product is easier to express.
Apr
23
comment Cross product angle formula
No, this one I didn't say:) The formula is good, and you can actually use it to get $\theta$. But it is usually easier to use the dot product.
Apr
23
answered Cross product angle formula
Apr
23
comment Derivative of map $f: S^n \to \mathbb{R}P^n$ is an isomorphism
$T_x\pi$ and $\Bbb RP^n$ are very concrete: if you choose appropriate coordinate systems, you can write it as the orthogonal projection matrix to a hyperspace. By the way,your claim about surjective maps seems plausible enough, however, I just could not manage to rigorously prove it..
Apr
21
revised Establish canonical isomorphism in Set category
edited body
Apr
21
comment Functor between Category and its Free Strict Monoidal Category
So, the functor has an object mapping part, this is given: $C\mapsto\Sigma(C)$, and a morphism mapping part. In $Cat$, the morphisms are the functors, so I guess your question basically is: 'What is $\Sigma(F)$ for a functor $F:C\to D$?'. Additionally, the statement goes beyond and claims a 2-cell mapping part, among others.
Apr
21
answered Establish canonical isomorphism in Set category
Apr
20
answered Prove that the infinite union of linearly independent sets is linearly independent