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2d
comment Subset vs. Proper subset
A proper subset is a special kind of subset. Any proper subset is also a subset. Not every subset is a proper subset. In the above example, $C$ is a subset of $A$ and it is also a proper subset of $A$.
2d
comment Is mathematics one big tautology?
no @Pacerier it's courtesy of my brain after reading "Proofs and Refutations".
Aug
28
answered Subspaces of an infinite dimensional vector space
Aug
27
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.
Aug
26
comment Is this always true about symmetric relations?
Try a direct argument to prove the claim. A very very direct argument.
Aug
26
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.
Aug
26
comment Circle topologically different from a line interval, torus from a rectangle (proof)
try drawing the pictures.
Aug
26
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.
Aug
26
comment Average length of a cycle in a n-permutation
What did you try?
Aug
19
awarded  Nice Answer
Aug
18
awarded  Necromancer
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
8
revised What is the average of no numbers?
added 19 characters in body
Aug
8
answered Cyclic subgroups and their cyclic groups
Aug
7
revised Why was set theory inadequate as a foundation to the emerging new fields and why category theory isn't?
deleted 6 characters in body
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
answered Open and closed sets in an arbitrary metric space example
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?