Jan
18
awarded Nice Answer
Jan
17
awarded Autobiographer
Jan
17
awarded Autobiographer
Jan
17
answered Ring homomorphism $\mathbb{Z}/8\mathbb{Z} \to \mathbb{Z}/5\mathbb{Z}$ implies $1=0$
Jan
17
comment Ring homomorphism $\mathbb{Z}/8\mathbb{Z} \to \mathbb{Z}/5\mathbb{Z}$ implies $1=0$
(and even that isn't a ring homomorphism, if you use the definition of "ring" that includes $1$ as part of its structure)
Jan
17
comment Infinity and the Maximum of Natural Number
@Magnus: It's interesting you would say that: when I learned the subject formally, extended real numbers were explicitly taught before measures and Lebesgue integration, as it makes it much easier to talk about such things.
Jan
17
answered A Set of Linear Equations Equal to Zero
Jan
17
answered Finding 3 variables a,b,c. 31a+30b+28c=365
Jan
17
comment Proving that S/I is a vector space
As an aside, your question makes it look like like you're actually having trouble with the ring structure on $S/I$.
Jan
17
answered Proving that S/I is a vector space
Jan
17
answered Determining subgroups of a finite field and their elements
Jan
17
comment is 2+2=5 possible?
I'm surprised this got so many downvotes, since this is a rather classic argument, often summarized as "2+2=5 for large values of 2".
Jan
17
answered Quadratic Forms in $n$ dimensions
Jan
16
answered Operator vs function
Jan
16
comment Is $\cos(1)^2$ irrational?
Aside: $( \frac{1}{10^k} ) = ( \frac{1}{10}, \frac{1}{100}, \frac{1}{1000}, \frac{1}{10000}, \ldots )$ tends to $0$ as $k \to \infty$ without ever reaching $0$, but $0$ manages to be rational anyways.
Jan
16
revised Does there exist an explicit formula for the coefficient of $x^k$ in the square of a polynomials?
added 403 characters in body
Jan
16
answered Does there exist an explicit formula for the coefficient of $x^k$ in the square of a polynomials?
Jan
16
comment slightly different definition of an ordered pair
I would add that it's probably better pedagogy to choose a definition where you don't have to invoke foundation to prove that it works.
Jan
16
comment What is the slowest growing function that cannot be proven to be total by PA?
But extremely fast doesn't actually mean fast enough. For a counterexample among modestly growing functions, consider $f(n) = \lfloor \log \log n \rfloor$ and $h(n) = \lfloor \sqrt{n} \rfloor$. Then to have $f(n) > j(m)$, you could need $n \sim m^{e/2}$ or larger.
Jan
16
comment What is the slowest growing function that cannot be proven to be total by PA?
Are you sure $f$ is actually faster growing than $j$?
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