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location Poland
age 24
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A PhD student of mathematics at Uniwersytet Wrocławski.


10h
comment Stack of records theorem for $C^0$ functions?
I'm not sure about the first question (I don't even know that a stack of records theorem is; care to explain exactly what you mean?), but as for the second question, it's not hard to show that any closed subset of ${\bf R}$ is the zero set of a smooth ($C^\infty$) function.
Jul
24
answered Question about Neighborhood basis
Jul
22
comment Probability of getting a right answer?
@Ovi: well, you can choose a number in the interval $[0,1]$, with uniform probability. ;-)
Jul
22
comment Probability of getting a right answer?
@Ovi: Maybe it's a trick question, and you're supposed to answer at random? ;-)
Jul
22
comment Probability of getting a right answer?
That's some lousy student.
Jul
19
comment Why are box topology and product topology different on infinite products of topological spaces?
My point was, thusly your example shows that the two topologies are (bar obvious exceptions) distinct, as opposed to being just an example.
Jul
19
comment Why are box topology and product topology different on infinite products of topological spaces?
More generally, in any product of nontrivial Hausdorff spaces, the subspace which is a product of two fixed points in each coordinate is discrete in box topology and compact in Tychnoff topology.
Jul
18
comment The standard role of intuitive numbers in the foundations of mathematics
@HandeBruijn: I'm a liberal mathematician: I think people can do any kind of mathematics they want, as long as they let others do the same. ;) I didn't mean to criticise you, I only wanted to avoid seeming like I believe intuitionism is somehow the "primitive" for mathematics. I do value a constructive proof more than a non-constructive one (and I loathe when people present as non-constructive proofs which are obviously constructive), but I don't believe we should restrict ourselves so much as to allow only constructive reasoning, at risk of losing beatiful theorems (or proofs).
Jul
18
comment The Dirac Delta Distribution $\delta_0 : D \to \mathbb R$ is not regular
I don't really know the conventions, but my guess would be that a distribution is a member of $C_c^\infty(\Omega)^*$, while restriction is to $C_c^\infty(\Omega\setminus\{0\})^*$ (by the natural restriction homomorphism). It also seems to make sense in the proof.
Jul
18
comment The standard role of intuitive numbers in the foundations of mathematics
@pablo1977: Therefore, I'm voting to close.
Jul
18
comment The standard role of intuitive numbers in the foundations of mathematics
@pablo1977: It seems to me like your question is not only very vague, but also impossible to answer for the reason that you seem to be looking for a very specific kind of answer which just can't be given in this case. You may consider accepting a convention an act of faith, but this act of faith is necessary for any science, and indeed, any activity. We need some rudimentary assumptions, some primitives with no definition which we simply accept. Without that we're suspended in limbo. That said, I'm far from being a proponent of intuitionism in mathematics. ;)
Jul
15
comment The standard role of intuitive numbers in the foundations of mathematics
@pablo1977: I'm not sure what you are asking about exactly. But generally reviewers should be experienced with the field, so that they can tell what consists a sufficient proof.
Jul
15
comment The standard role of intuitive numbers in the foundations of mathematics
@pablo1977: My point was exactly that there are no exact criteria, just like there are no exact criteria as to what is and isn't a proof. As to whether or not mathematics is science, many would not agree with you. See for example this thread: math.stackexchange.com/q/287701/30222 .
Jul
15
comment The standard role of intuitive numbers in the foundations of mathematics
@pablo1977: It is not reliable in the sense that you can't rigorously show that the foundations are consistent (although the same is true for all sciences, I guess). Most mathematicians believe that they are, but this is a problem with all kinds of foundations (not just mathematical): you must take some primitives for granted (or risk circularity or infinite regress). For the most part, foundations can be reduced to basic (naïve) arithmetic or naïve set theory, and there's no solid starting point for those beyond our intuition coming from some real-world experience. Mathematics is not science.
Jul
15
answered The standard role of intuitive numbers in the foundations of mathematics
Jul
13
comment Covering $S^{n-1}$ with $n+1$ closed sets containing no antipodal points
Beat me to it (although to get the usual embedding of $S^n$, the mapping you mention shouldn't be an isometry). Still, as far as I'm concerned, any argument explicitly using coordinates is far more messy than the abstract one (there clearly is a regular simplex inscribed in any $n$-sphere and proving it for a specific sphere seems akin to proving an instance of Fubini's theorem every time we use it).
Jul
13
comment Probability of identical twins
@badmax: It helps in that it allows anyone potentially willing to help you to just focus on the question itself, as opposed to guessing details you have omitted.
Jul
13
comment Probability of identical twins
You probably meant to say that $MM$ and $FF$ stand for the event that, in a random pair of twins, both are male (or female).
Jul
10
comment Question about different defintions of isometry on a Hilbert space
It's kind of strange you've not heard of the real polarisation identity. I always found it way more intuitive and natural than the complex one (I always have hard time deriving that when I need it).
Jul
10
comment Formally show that the set of continuous functions is not measurable
Just notice that any continuous function on ${\bf R}$ can be modified on any cocountable set (indeed, on any nonempty set) so that the result is discontinuous.