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15h
comment Is an non-invertable matrix an linear operator?
once bases are chosen, any matrix induces a linear transformation (of course the dimensions need to match).
1d
comment Brouwer fixed-point theorem on non-convex sets
your question (I believe) is discussed in detail in math.stackexchange.com/questions/323841/…
1d
comment On the properties of an interesting set on the real line…
"every element of $K$ has a unique decimal representation" is hardly an interesting property. The other properties you mention are of some interest, but you will have to find some really fabulous properties of your set to merit any further discussion. Also, the fact that your set depends on a decimal expansions diminishes its quality.
2d
comment “Notes on Set Theory” - Badly Written?
not quite answering your question, but if you are looking for a good online introductory text on set theory and logic, you may wish to try staff.science.uu.nl/~ooste110/syllabi/setsproofs09.pdf
May
19
comment Question about limit and dividing by zero
that's the spirit!
May
19
comment Question about limit and dividing by zero
no @Rzeta, not at all.
May
19
comment Can a nonempty set ever equal its Cartesian product with another set?
OP seems to be asking about actual equality, not bijective correspondences.
May
18
comment Brouwer's fixed-point theorem and the intermediate value theorem?
Because if $f(x)>t$, then $f(x+h)>t$ for sufficiently small $|h|$, by continuity of $f$.
May
17
comment Little confused about the constraint of Injective Functions and Surjective.
Michael's answer is all the explanation required.
May
17
comment Little confused about the constraint of Injective Functions and Surjective.
no, this is not all correct. In fact, it is mostly incorrect.
May
17
comment What does it mean for a set to exist?
If the anonymous downvoter cares to elaborate, I'm all ears.
May
15
comment Is it possible to make uniform irrational numbers from nonuniform irrationals?
what is a nonuniform irrational??? what do you mean shuffle it?
May
13
comment Is such set a group?
having a binary operation on a set means the set is closed under the operation. That is the meaning of being a binary operation on a set.
May
12
comment The length of a point and the interval
The problem is with definitions. If you don't define your concepts clearly, then you can't expect to ask a precise question, let alone for a fallacy to be identified. Prior to identifying a fallacy you must formalize your arguments.
May
10
comment Intersection of open sets in $\mathbb{R}$
@Stromael no, there are topological spaces with the property that the open sets are closed under arbitrary unions. Discrete and indiscrete ones for example, but also many other spaces.
May
4
comment Construct a non-linear function that shows that the intervals $[2,4]$ and $[10,22]$ have the same cardinality
to answer some homework questions, I guess. This is hardly of any importance.
May
4
comment Prove $\bigcap S$ exists for all $S \ne \emptyset$. Where is the assumption $S \ne \emptyset$ used in the proof?
Which set do you suggest then that $\bigcap \emptyset $ would be?
May
3
comment Write 100 as the sum of two positive integers
The Bezout coefficients for positive integers are guaranteed to have different signs.
May
3
comment What if we change the def of limit as following
because it leads to a different notions, and a useless one in fact.
May
3
comment Simple dice probability question
how many sides does each dice have? What is the probability of each of the sides of each dice? Without that information it is impossible to answer the question.