7,852 reputation
11739
bio website
location
age
visits member for 2 years, 8 months
seen 31 mins ago

Jan
17
answered What's your favorite proof accessible to a general audience?
Jan
17
comment What's your favorite proof accessible to a general audience?
Keep in mind the definition of "general audience". Will a general audience understand exponent rules with irrational exponents? Will they even appreciate what an "irrational number" is?
Jan
17
comment What's your favorite proof accessible to a general audience?
Even explaining (properly) what a real number is would take about 20 minutes at least.
Jan
17
comment What's your favorite proof accessible to a general audience?
@GabrielH hsm.stackexchange.com/questions/384/…
Jan
17
comment How can I work out if a certain group presentation implies a certain relation?
@Myself Providing counterexamples was the type of answer provided on the original question - I'm specifically interested in "direct" approaches with the presentation.
Jan
17
asked How can I work out if a certain group presentation implies a certain relation?
Jan
16
answered Proving that the series 1 + … + $1 / \sqrt{x}$ < $2 \sqrt{x}$
Jan
15
comment Confused about complex numbers
The short version: if $z$ is complex, then $z^{0.5}$ is meaningless.
Jan
15
comment An example of a problem which is difficult but is made easier when a diagram is drawn
Why would the pair $(P, \ell)$ be unique? In fact, since for any $\ell\in L$, there is a point $P\in S$ on it (and thus having distance zero from it), just pick any $\ell \in L$ and any $P$ on it and you have an optimal pair. What am I misunderstanding?
Jan
15
comment Do 'symmetric integers' have some other name?
I'm not sure it is, the book isn't a textbook or anything, the system is just developed as an example, really.
Jan
14
comment Do 'symmetric integers' have some other name?
There's a book called Negative Math in which the author develops such a system and explores some of its properties, although it's not very in depth.
Jan
10
reviewed Reject Give a direct proof of the fact that $a^2-5a+6$ is even for any $a \in \mathbb Z$
Jan
6
comment If $F = (V,E)$ is a group of trees , $h(F) \equiv \mid V \mid \pmod 2 $?
@PaulB. Well, it implies that a tree has an odd number of vertices iff it has an even number of edges, and has an even number of vertices iff it has an odd number of edges. Count $|V|$ by summing up the number of vertices in each tree. Modulo $2$, you can forget about the trees with an even number of vertices...
Jan
5
answered If $F = (V,E)$ is a group of trees , $h(F) \equiv \mid V \mid \pmod 2 $?
Jan
3
comment Magical properties in “2015”?
I'd be surprised if there are any interesting mathematical patterns at work here. There is a particular set of numbers which can be obtained by substituting the four arithmetic operators in every possible way into the expression $((((((((1\circ2)\circ3)\circ4)\circ5)\circ6)\circ7\circ)\circ8)\circ9)$. We can go around defining sets of numbers all day, but most of them won't have any interesting internal structure.
Jan
2
comment Is there an equation that will graph a line segment?
Not that this isn't interesting, but I always feel like absolute values are "cheating", in these questions. The obvious answer to these questions is to define a function piecewise, but that's unsatisfactory - what we want is something "defined by a formula". But the absolute value function is itself defined piecewise, so we've really just hidden the piecewisedness of the definition under the rug. Of course, in this case there really is no "pure formula" for the desired function, so a solution involving absolute values is still of interest.
Dec
31
comment Determine angles of triangle given nothing (no scientific calculator) but triangle sides.
@CoronaSalad In fact, your problem is equivalent to calculating $\cos^{-1}$ in the sense that any method that allows you to calculate $\cos^{-1}$ allows you to solve your problem and vice versa. So the two problems are "equally difficult".
Dec
31
answered Deduce $\lvert ab\rvert = \lvert ba\rvert$ for all $a,b\in G$ where $G$ is a group.
Dec
29
comment Are there rigorous formulation and proof of the pigeonhole principle?
To be clear, just accepting the pigeonhole principle as an obvious fact is rigorous, because it's so patently obvious. You want a formal proof, but formality and rigor are distinct notions.
Dec
26
comment Abstract alphabets by Kolmogorov??
An infinite alphabet is what it sounds like - an infinite set of symbols.