81,748 reputation
4107207
bio website henning.makholm.net
location Copenhagen, Denmark
age 40
visits member for 2 years, 11 months
seen 1 hour ago

I'm a computer scientist by training (Ph.D. in programming language technology, 2003), currently working in industry. Real mathematics is more of a hobby.

In general, don't assume I necessarily know what I'm talking about, unless it's about computer science or formal logic. I dabble in various other fields that I've never taken courses in, mostly just by extrapolating from Wikipedia.


8h
answered Is it the case that for all sets $A, B, C,$ and $D$, $(A \times B) \cup (C \times D) = (A \cup B) \times (C \cup D)$?
11h
revised How to prove indicator function, step function, and then for sequences of step functions?
edited tags
11h
comment Contribution of each variable in multiple linear regression
How about $\frac{a_1^2}{a_1^2+a_2^2}$, which measures how much the gradient is in the $X_1$ direction? In most contexts $a_3$ is probably not that relevant, since it's just a common offset.
21h
awarded  Enlightened
22h
awarded  Nice Answer
1d
comment Are inverse matrices unique?
(+1) It can also happen if instead of matrices we consider linear transformations $V\to V$. If $V$ is infinite-dimensional, then there are transformations with many left-inverses and no right-inverse, or vice versa.
1d
comment Are inverse matrices unique?
(Ignore the link in the above comment. It assumes that every right inverse has a right inverse itself).
1d
comment Are inverse matrices unique?
But how do we know that $GL(n,\mathbb F)$ is a group in the first place? That's because we already know matrix inverses behave like they ought to.
1d
comment Are inverse matrices unique?
Your calculation depends on $B$ being a two-sided inverse (or at least on $A$ having some left inverse), which seems to deserve a proof of its own. (E.g., here)
1d
awarded  Enlightened
1d
awarded  Nice Answer
1d
answered Reducing $ab' + cb + ac$ to $ab' + cb$
2d
comment the use of Cartesian product
It's amazing what one can get upvotes for.
2d
comment Product of two negative numbers is positive
It's not a matter of proof -- but a convention that happens to make the laws of arithmetic hold with greater generality than other possible conventions for the product of negative numbers would.
2d
comment What are some 'conceptualizations' that work in mathematics but are not strictly true?
@Dustan: What this comes down to is whether there is any definable set the ZFC proves non-measurable at all -- i.e. whether there is a formula $\varphi(x)$ such that ZFC proves $$\exists_1 x.\varphi(x) ~\land~ \forall x.\varphi(x)\to x\text{ is not measurable}$$ If there is such a formula, then $\bigcup_{x\subseteq \mathbb R, \varphi(x)} x$ can (trivially) be proven to exist by ZF, whereas ZFC will additionally prove it is non-measurable.
2d
answered the use of Cartesian product
2d
comment paths from from point A to point B with length 8
@user2838619: Yes, just mirror the relevant portion of the path in the diagonal line between A and B. So in your example path RRUURRUU, flipping the initial RRUU portion will produce UURRRRUU. And flipping the entire path RRRUURUU produces UUURRURR.
2d
comment Using all types of fractions
In actual usage, the notation $A\frac BC$ means a mixed fraction exactly when $A$, $B$ and $C$ are all bare numbers. If any of them is a variable or an arithmetic expression, then it means a product. So when one evaluates, for example, $2\frac{2+2}5$ step by step, one needs to careful to write the next step as $2\cdot\frac{4}{5}$ rather than $2\frac45$ to avoid suddenly writing something that will be read as a mixed fraction.
2d
revised paths from from point A to point B with length 8
added 4 characters in body
2d
answered paths from from point A to point B with length 8