Reputation
153,451
Next tag badge:
99/100 score
50/20 answers
Badges
10 148 293
Newest
 Enlightened
Impact
~1.5m people reached

1h
comment Find all functions f with the following two properties
You can't use $x=-k$ because $x$ and $k$ must both be $\ge 0$. Also, it seems that $f$ can be arbitrary on $[0,k)$
1h
comment (Theoritical Question) Multiply two negatives, get a positive, but…
Somehow you do need addition beause $-a$ is defined as a/the number that when added to $a$ produces $0$. And of coursde you also need the distributive law, which is the only way how addition and multiplication interfere
2h
comment Distances within Coding Theory
The statement is not true unless we impose the condition that $a,b$ be nonnegative integers.
2h
answered Distances within Coding Theory
3h
comment Cauchy-Schwarz Inequality without using $\langle a x,y\rangle=a\langle x,y\rangle$
Using "all axioms except one" without explicitly listing the remaining axioms is hard to work with when there are different sets of axioms possible
3h
comment Difference between ${2\over 9}$ and ${22\over 99}$?
These are just two different fractions that represent the same rational number.
3h
answered Number theory problem and Diophantine Equations
19h
comment Show that there is a metric space that has a limit point, and each open disk in it is closed. Collecting examples
@columbus8myhw No. The open disk of radius $1$ around $1$ is not closed
20h
answered If $E$ and $F$ are disjoint closed subsets of a metric space $(X,d)$, then is $dist~(E,F) >0$ always?
1d
comment vercongent sequences
@RickyDemer Any sequence in an empty space is vercongent, convergent, and married to a unicorn
1d
comment Prove that every integer $n\geq 7$ can be expressed as a sum of distinct primes.
The accepted answer to math.stackexchange.com/questions/1382803/… contains a short proof of Richert's result.
1d
comment From the perspective of the multiverse theory, would maths “work the same” in every possible Universe?
The math should be the same, but not the same theories may be applicable to the same phenomena. Even in our home universe we may have that $1$ drop of water plus $1$ drop of water is still just $1$ (bigger) drop of water. This doesn't show that $1+1=1$ instead of $=2$, it shows that for this phenomenon, addition of natural numbers is not a suitable model.
1d
comment How to prove that any natural number $n \geq 34$ can be written as the sum of distinct triangular numbers?
Interestingly, the same question with primes (so using Bertrand's postulate) popped up today as well, I think
1d
comment Prove that every integer $n\geq 7$ can be expressed as a sum of distinct primes.
Richert's theorem does use positive primes only. What you saw in the proof was that sums of the form $\sum_{k=1}^n\epsilon_kp_k$ with $\epsilon_k\in\{-1,1\}$ cover all integers (of correct parity) in a large interval. Adding $\sum_{k=1}^np_k$ produces all even numbers in a suitable interval where all coefficients are in $\{0,2\}$. Division by $2$ produces the claim.
1d
awarded  Enlightened
1d
comment How to show the inequality is strict?
Actually, add $\pm$ (or allow complex $c$)
1d
answered How to show the inequality is strict?
1d
comment how to prove that $ \lim x_n^{y_n}=\lim x_n^{\lim y_n}$?
Note that $x^y=\exp(y\ln x)$ (or how else do you define arbitrary powers?
1d
answered evaluate $\lim_{n\to\infty}\sum_{r=1}^{n-1}\frac{e^{r/n}}{n}$
1d
comment Some questions about Banach Tarski proof
@idkwptc I think I expressed very clearly that there is only a countable number of poles. There is a $2:1$ map from the set of poles to $H\setminus\{1\}$