4,458 reputation
1335
bio website
location
age
visits member for 4 years, 3 months
seen 9 hours ago

Dec
14
reviewed Approve Homothetic transformation
Dec
12
comment What's the difference between a bijection and an isomorphism?
In short, a bijection (or -jection) is a kind of function on sets. An isomorphism (or -morphism) is a kind of function that is structure preserving. Or rather one term is in the language of set theory, the other is in category theory. Underlying all isomorphisms is some bijection, but a bijection doesn't necessarily preserve structure in the category you care about. If your category is Sets, then they're the same.
Dec
8
comment Is 128 the only multi-digit power of 2 such that each of its digits is also a power of 2?
Don't forget to also rule out 8.
Dec
8
awarded  Caucus
Dec
5
awarded  Nice Answer
Dec
3
comment Is it possible to simulate a floor() function with elementary arithmetic?
@ChristianSemrau the given ops do not allow complex math (exact, not floating point) or arbitrary roots of unity either. The true answer is either 'no' because of the reason given in the top answer, or 'yes' because the domain is integers and integer division already gives the floor.
Dec
2
revised Is it possible to simulate a floor() function with elementary arithmetic?
typo
Dec
2
comment Is it possible to simulate a floor() function with elementary arithmetic?
Since all your ops are on integers, the output of each op will be integers. The default implementation of integer division and so will be to 'round to 0' which is equivalent to 'floor' on non-negative integers. Which means you don't need a special 'floor' function because you already have it by default.
Dec
2
answered Is it possible to simulate a floor() function with elementary arithmetic?
Dec
2
answered Is it possible to simulate a floor() function with elementary arithmetic?
Nov
8
answered Reference textbook about proof techniques
Nov
8
revised Reference textbook about proof techniques
proof -> proofing
Sep
30
awarded  Explainer
Sep
29
comment Why are real numbers useful?
Use the binomial distribution.
Sep
25
comment Understanding why Hall's marriage theorem $\Leftrightarrow$ Dilworth's theorem
robertborgersen.info/Presentations/GS-05R-1.pdf gives a number of proofs around all these theorems.
Sep
25
comment Analytic Proof Of ${n\choose r}={n-1\choose r-1}+{n-1\choose r}$
I would call this an 'algebraic' proof. An 'analytic' proof would more likely be a proof using generating functions. Of course everything uses algebra to some extent, but the major category of a proof is the primary strategy.
Sep
25
comment Sum of sequence of cubes and summation on the upper index
$k^3 = 6{k \choose 3} + 3 k^2 -2k $ (I got this by expanding out ${k \choose 3}$). Now eliminate the $k^2$ using ${k \choose 2}$. Then again for the leftover $k$ term. Now, if you sum the LHS, you sum the RHS. But by the stated thm, you can calculate the sum of the RHS.
Sep
25
comment General term of $(1+x)(1+x^2)(1+x^3)…$?
If you want to calculate these without calculating coeffs of the gf directly, I think the best formula is the recursive one in the OEIS: a(n)=(1/n)*Sum_{k=1..n} b(k)*a(n-k), with a(0)=1 and b(n)= A000593(n) = sum of odd divisors of n.
Sep
22
awarded  Good Answer
Sep
20
awarded  Nice Question