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Apr
17
comment What is the determinant of the sum of a diagonal matrix and a matrix of ones?
@deinst Strictly speaking, the case that at least one of the diagonal entries is $1$ (i..e, singular $A$) is not covered in (6.2.3)
Apr
17
answered Verbal Reasoning (Puzzle)
Apr
17
revised To prove that $I = \{\,(n,m) \in \Bbb Z \times \Bbb Z : n,m $ are even $\}$ is not a maximal ideal of $ \Bbb Z \times \Bbb Z $.
added 4 characters in body; edited title
Apr
17
answered To prove that $I = \{\,(n,m) \in \Bbb Z \times \Bbb Z : n,m $ are even $\}$ is not a maximal ideal of $ \Bbb Z \times \Bbb Z $.
Apr
17
revised How do I prove this Limit?
deleted 38 characters in body
Apr
17
answered How do I prove this Limit?
Apr
17
answered Prove $x^7+3x^5+1$ has exactly one real root using Bolzano's theorem and the MVT.
Apr
17
comment Existence of a vector in a given basis of a vector space with increasing coordinates
Certainly, $\alpha=\beta=0$.
Apr
17
answered Let $I = \{a +\sqrt2b \in \Bbb Z[\sqrt2] : a$ and $b$ are both multiple of $5\}$.
Apr
17
answered Countably Infinite Collections of Sets
Apr
17
answered Elements of $\mathbb{Z}/(n)$
Apr
17
answered $\{\infty\}$ open in $\mathbb N\cup\{\infty\}$ with $d(a,b)=|\arctan a-\arctan b|$?
Apr
17
revised $\bigcup \alpha$ where $\alpha$ is a finite ordinal.
edited body
Apr
17
answered $\bigcup \alpha$ where $\alpha$ is a finite ordinal.
Apr
17
answered Every Cauchy Sequence in the real number line converges
Apr
17
revised Every Cauchy Sequence in the real number line converges
deleted 7 characters in body
Apr
17
comment Is $f\colon Y'\to Y$ continuous?
Is $T$ assumed bijective or are the $T^{-n}x$ assumed to be sets? Or is in fact $T$ the translation map?
Apr
17
comment How to write the family of sets whose elements are the sets in a sequence of sets
For me both are the same as the third: a function with domain $\mathbb N$. Whether we call it function or sequence or family (and use different notations accordinly) is matter of taste or a means to emphasize one aspect or other of the same thing.
Apr
17
answered Restriction of topological ring isomorphism
Apr
17
comment How to write the family of sets whose elements are the sets in a sequence of sets
I usually write $\{X_n\}_{n\in\mathbb N}$, whereas $\{\,X_n\mid n\in\mathbb N\,\}$ would be the set of the sets occuring in the sequence (and the family). - Then again, "sequence" and "family" (with index set $\mathbb N$) are essentially the same concepts ...