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Aug
5
answered Are sequences properly denoted as $\subset$ of a set, or $\in$ a set?
Aug
2
answered Prove that if $\forall A \in \mathcal F (B\subseteq A)$ then $B \subseteq \bigcap \mathcal F $
Aug
2
awarded  Good Answer
Jul
31
comment Can we parameterize a topological space?
any bijective continuous function $f\colon X\to Y$ can be thought of as a parametrisation of $Y$ by $X$.
Jul
31
comment Stuck on large numbers
what does the title have to do with the question???
Jul
31
answered Does $G\times H\cong G'\times H'$ imply $G\cong G'$ and $H\cong H'$?
Jul
31
comment Pathological Question involving $C^1$ Criterion for Differentiability
how about $f\colon \mathbb R^2 \to \mathbb R$ given by $f(x,y)=xy$ if $x,y\in \mathbb Q$ and $f(x,y)=-xy$ otherwise ?
Jul
30
comment Continuity Must Hold in an Entire Open Set?
yes Amitai, something like that :)
Jul
30
answered Continuity Must Hold in an Entire Open Set?
Jul
27
comment “continuously differentiable $\subseteq$ Lipshitz continuous” with $f(x) = x^2$
"over a closed and bounded set"!!!
Jul
26
answered Why do the integers, rationals and any countable set have zero measure?
Jul
26
comment Intuition for the Cauchy-Schwarz inequality
@Mehrdad that student can be shown this fact, or requested to clarify the intuition in an exercise.
Jul
26
comment Intuition for the Cauchy-Schwarz inequality
beware a circular argument: it is the CS inequality that allows one to define $\theta$ in the first place.
Jul
26
comment Intuition for the Cauchy-Schwarz inequality
@Mehrdad the relation to the cosine (law) may be not the best way to see that. I like to think of it in terms of orthonormal basis. Given an orthonormal basis, any vector $u$ is simply $\sum_i (u\cdot v_i) \cdot v_i$ by a trivial computation which has nothing to do with CW or the law of cosines. This trivially shows that the dot product gives the components of a vector. When teaching these things I like to use the law of cosines to motivate the definition of the standard inner product. Then CS is shown to relate to a law of cosines (kind of) for any inner product.
Jul
26
answered Intuition for the Cauchy-Schwarz inequality
Jul
23
revised Why the surface of the sphere is not a Euclidean space?
edited body
Jul
22
comment Finite free objects
what do you mean by trivial here? As the question stands it highly unclear what you are looking for.
Jul
22
answered Can $1=0$ ever make sense?
Jul
22
comment Can $1=0$ ever make sense?
@JoshuaLaJeunesse I edited your question further. I hope this is still in line with what you have/had in mind.
Jul
22
revised Can $1=0$ ever make sense?
added 207 characters in body; edited title