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1d
comment Can we add an uncountable number of positive elements, and can this sum be finite?
You misread Michael's statement. He said if any of those intersections is infinite, then the sum is automatically infinite. If they're all finite, then there are only countably many (positive) elements of $S$.
1d
comment Can we add an uncountable number of positive elements, and can this sum be finite?
Although, tiny quibble: this definition fails to allow for the same number to occur twice in a sum.
1d
comment Can we add an uncountable number of positive elements, and can this sum be finite?
@AyushKhaitan Blazej's comment is referring to the case of including negative numbers. Michael Hardy's definition is perfectly sensible for the case of summing up a system of only positive numbers.
1d
reviewed Approve Can we add an uncountable number of positive elements, and can this sum be finite?
Aug
25
comment Higher infinities without Set Theory
What do you mean by outside of set theory? The family of functions $\mathbb R \to \mathbb R$ has cardinality $2^{\mathfrak c}$. If you restrict to continuous functions or nicer, then yes, it goes down to $\mathfrak c$, but if you restrict to merely Lebesgue measurable functions, which I think are of reasonable interest outside of set theory, you still get $2^{\mathfrak c}$.
Aug
25
comment Inverse images of ideals
@IvoTerek That doesn't make it much more difficult; the use of unity just allows one to abbreviate what it means to have $J'=R$. Editted accordingly.
Aug
25
revised Inverse images of ideals
added 97 characters in body
Aug
25
comment Absolute Value Property of Field of Real Numbers
The proper negation of the statement "$-a \le b \le a$" is that "either $b < -a$ or $b > a$".
Aug
25
answered Inverse images of ideals
Aug
23
comment Can a non singular matrix of order $k\times k$ be changed into singular by changing exactly one element or vice versa?
ah, A.G.'s comment addresses my concern.
Aug
23
comment Can a non singular matrix of order $k\times k$ be changed into singular by changing exactly one element or vice versa?
Is there something which ensures that the determinant polynomial is not a nonzero constant?
Aug
6
comment Why does $\sum_{\sigma\in S_n}q^{\ell(\sigma)}=\frac{(1-q)(1-q^2)\cdots(1-q^n)}{(1-q)^n}$?
That wouldn't be surprising! ;)
Aug
6
revised Why does $\sum_{\sigma\in S_n}q^{\ell(\sigma)}=\frac{(1-q)(1-q^2)\cdots(1-q^n)}{(1-q)^n}$?
deleted 8 characters in body
Aug
6
answered Why does $\sum_{\sigma\in S_n}q^{\ell(\sigma)}=\frac{(1-q)(1-q^2)\cdots(1-q^n)}{(1-q)^n}$?
Jun
14
comment Suppose $F$ is a field and the irreducible polynomial over $F$ of $x$ is of odd degree.
That's correct.
Jun
8
comment Imitating smaller Rubik's cubes with bigger ones.
I was talking about in the first paragraph
Jun
8
comment Imitating smaller Rubik's cubes with bigger ones.
I'm not reading your link since I'm on my phone, but you did skip mention of the step where you fix the positions that you might get on the "3-cube" that are impossible on a normal 3-cube.
Jun
6
answered Finite “snakes” in a connected space
Jun
6
comment What is the idea behind a projection operator? What does it do?
What's wrong with the current answers? Sure, the most popular one is a bit tongue in cheek (simply describing what idempotence means in a more colloquial setting), but the answers below it do describe projection mathematically in pretty clear detail.
Jun
5
comment Can any commutative ring of characteristic $p\in\mathbb P$ be written as the form $R/(p)$ with $R$ being a ring of characteristic $0$?
I highly doubt there's a universal lift to characteristic zero as you describe.