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Jun
2
comment what is the symbol generally used for whole numbers?
@rschwieb I stand corrected (and I'm shocked). Re-defining 'whole' is just weird.
Jun
2
comment what is the symbol generally used for whole numbers?
It is not true that the standard notation is $0\in \mathbb N$. There is no standard agreement concerning the naturality of $0$.
Jun
2
comment what is the symbol generally used for whole numbers?
When mathematical convention is consistent and well-established and well-justified and makes perfect sense, there really is no justification to deviate. Nobody uses $W$ for the whole numbers. There is no difference between the whole numbers and the integers. The whole numbers are denoted by $\mathbb Z$. The natural are denoted by $\mathbb N$, though whether or not $0$ is considered natural is not agreed upon.
Jun
2
comment what is the symbol generally used for whole numbers?
@rschwieb I will be very surprised if the american schools redefine the meaning of whole numbers. Whole, or integer (both words mean the same) have a clear meaning, i.e., having no fractional part. Clearly $-5$ is a whole number.
Jun
2
comment what is the symbol generally used for whole numbers?
the whole numbers are not the same as the natural numbers. Not to OP, and not to anybody.
Jun
2
answered Why doesn't the Taylor series always converge?
Jun
1
comment Is a subset of an inner product space also an inner product space?
of course you can choose any subset, so also one that is not a subspace.
Jun
1
awarded  Nice Answer
Jun
1
comment Wrong intuitive understanding of a limit?
@Ixrec I don't think people were worried calculus would turn out to be wrong. The thing is that due to lack of rigour people were not even agreeing on what the simplest things were (e.g., what a function is). Nonetheless, the objects of main study were solid enough for it to be clear enough that while a formalism is lacking, it is only a question of time before it is found. People realised the importance of finding a formalism, but not because they needed convincing of consistency.
Jun
1
answered Wrong intuitive understanding of a limit?
May
31
answered Is the infinitesimal approach good.
May
29
comment Impossible Math Riddle
what did you try? did you at least start off by decomposing $72$ as the product of three integers? Did you then consider the possible sums? Did you go through some of those possibilities? did you eliminate impossible ones. Did you look at what's left? Maybe then the final clue will make sense to you.
May
28
comment Coproduct of groups explanation
can you perhaps give the precise quote, with sufficient information to really discern what is going on?
May
28
comment Is $O(n)$ normal in $GL(n)$?
@AsafShachar, almost any choice of $S$ and something in $O(n)$ would have shown that. To show that a universal claim does not hold you go for counter examples, not generic proofs.
May
28
comment Is $O(n)$ normal in $GL(n)$?
did you try conjugating some orthogonal matrices and see if you still get an orthogonal matrix?
May
28
revised Is this a correct way to think about specific examples of groups using the category theory definition?
added 4 characters in body
May
28
answered Is this a correct way to think about specific examples of groups using the category theory definition?
May
28
answered Prove the isomorphism of categories $Fun(\mathcal{A}\times\mathcal{B},\mathcal{C})\cong Fun(\mathcal{A},Fun(\mathcal{B},\mathcal{C})),$
May
27
reviewed Approve how to show that$ n<{2n \choose n}$ in sets
May
27
comment What is the mathematical difference between group and category?
@berci (what PyRulez said +) the best you can get is an adjoint equivalence with FG=id, but not GF=id due to the fact that when passing from the category of one object all isos categories to the category of sets, the information lost is the name of the single object. The functor int he other direction must make up an arbitrary name for the single object in order to view a group as a single object all isos category.