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May
24
comment Basis and dimension of the span of the vectors (0, 0, 0), (9, 0, 0), (8, 1, 0), (1, 8, 9)
It is asking you to find a linearly independent subset of $S$ that has the same span as $S$.
May
23
comment Proving that $a \dot{-} (b+1) = (a \dot{-} b) \dot{-} 1$
@Nagase You prove it using the distributive and commutative laws. Look at $(a-b)-1-(a-(b+1))$ and show it equals $0$.
May
23
comment Proving that $a \dot{-} (b+1) = (a \dot{-} b) \dot{-} 1$
If $a\geq b+1$, then $a\dot{-}(b+1)=a-(b+1)$ and $(a\dot{-}b)\dot{-}1=(a-b)\dot{-}1$. But, $a-b\geq 1$. So, $(a-b)\dot{-}1=(a-b)-1$, which is the same as $a-(b+1)$.
May
23
comment Proving that $a \dot{-} (b+1) = (a \dot{-} b) \dot{-} 1$
I wouldn't think induction works. You could try cases: $a\geq b+1$, $a\geq b$ but $a<b+1$, $a<b$.
May
23
reviewed Close Is $\mathbb{Z}[2\sqrt{2}]$ a PID?
May
23
reviewed Close Doesn't axiom of choice only apply to countable many groups?
May
23
reviewed Close What result multiplying 2 3D-vectors?
May
22
answered Determine whether $f(x)$ is increasing or decreasing
May
21
comment Homotopy of a pair
@user135988 It is not the case that $\pi_1(X,A)$ is trivial for all $X$ and subspaces $A$. Just let $A=x_0$.
May
21
comment Homotopy of a pair
@user135988 Because $I^n$ is a contractible space. Given any space, $Y$, any map $I^n\rightarrow Y$ is homotopic to a constant map, as long as you have no restrictions on the homotopy. In your case as long as the map is contained entirely in $A$, you have no restrictions on the homotopy.
May
20
revised Homotopy of a pair
added 138 characters in body
May
20
answered Homotopy of a pair
May
19
comment Can a nonempty set ever equal its Cartesian product with another set?
If $T$ is the one element set, yes. I suppose they might not be $\textit{equal}$, depending on your definitions.
May
19
comment What does “all but” means? Rudin 3.2
It means that that there are only a finite number of points in $P_n$ that are not in a given neighborhood.
May
19
comment Prerequisites for learning general topology
There is a free book "Topology Without Tears" u.math.biu.ac.il/~megereli/topbook.pdf I would suggest reading Chapter 5 before Chapter 4.
May
17
comment (basic?) isomorphism of topological K-theory and reduced K-theory
That's one way to think of it. You can also think about the map of pairs $(X,\emptyset)\rightarrow (X^+,\tilde{pt})$.
May
16
comment Definite integral of absolute value is zero iff . . .
You are using contrapositive, not contradiction.
May
14
comment Interior/boundary of unit diagonal
The interior of a subset is the largest open set contained within it. Open subsets of $\mathbb{R}^2$ are unions of open discs. If the diagonal had a nonempty interior, it would have to contain at least one open disc.
May
13
answered If $T : V \to k$ is not the zero map, there is $v \in V$ such that $T(v) = 1$.
May
13
comment Interior/boundary of unit diagonal
I didn't say the boundary would be empty, only its interior.