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1d
comment Derivative of any $x$ which is not zero.
contrary to some comments above, many thumbs up to you @DanielaMorais on learning these things on your own (if that is what you do). Learning to cope with written material on your own is something you should start doing very early on, no matter how unintuitive the stuff is. By all means, do continue to tackle anything that comes your way in any way that you see fit.
1d
comment Is this always true about symmetric relations?
Try a direct argument to prove the claim. A very very direct argument.
1d
comment Circle topologically different from a line interval, torus from a rectangle (proof)
if you remove a point from a line, say the $X$-axis in $\mathbb R^2$, then you get two open half-lines, not a single line.
1d
comment Circle topologically different from a line interval, torus from a rectangle (proof)
try drawing the pictures.
1d
comment Circle topologically different from a line interval, torus from a rectangle (proof)
Removing any of the internal points of an interval leaves two connected components. Removing an end-point leaves one connected component.
1d
comment Average length of a cycle in a n-permutation
What did you try?
Aug
13
comment How to notate a sequence of decimals
there is no such notation. You are free to make up anything you want.
Aug
13
comment Example of a path $\gamma:[a, b] \to \Bbb R^2$ whose image is not a thin curve?
@Ishfaaq you may have read that there is no continuous bijection $[0,1]\to [0,1]\times [0,1]$.
Aug
13
comment Example of a path $\gamma:[a, b] \to \Bbb R^2$ whose image is not a thin curve?
The Peano curve is very much continuous. So, you may wish to rephrase your question.
Aug
7
comment Why was set theory inadequate as a foundation to the emerging new fields and why category theory isn't?
@PouyanMoradifar where do you see any issue with defining that category within ZFC?
Aug
5
comment Intuitively, what is the difference between homeomorphism and diffeomorphism? Significance?
@TimothyCarson do you know what a smooth manifold is? what the definition of diffeomorphism is?
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
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
27
comment “continuously differentiable $\subseteq$ Lipshitz continuous” with $f(x) = x^2$
"over a closed and bounded set"!!!
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
22
comment Finite free objects
what do you mean by trivial here? As the question stands it highly unclear what you are looking for.