dREaM
Reputation
371/400 score
3 38 88
Impact
~298k people reached

# 4,806 Actions

 May7 answered Finite abelian groups of order 100 May7 answered Group of $2n$ elements, $n$ odd, is not simple May6 revised At the point $\sqrt{2}$ in the real line, does *every* n-ball around that point contain a rational? deleted 3 characters in body May6 answered At the point $\sqrt{2}$ in the real line, does *every* n-ball around that point contain a rational? May6 comment Formula for $r+2r^2+3r^3+…+nr^n$ Oh dayum, this is nice. May6 comment Formula for $r+2r^2+3r^3+…+nr^n$ If you take it to infinity then yes. May6 answered Prove that if $\{1^5,2^5,\ldots, (pq)^5\}$ is a complete residue system mod $pq$, then $\{1^5,2^5,\ldots,p^5\}$ is a complete residue system mod $p$. May5 comment What are the primary disadvantages of Dummit and Foote's abstract algebra text (3rd ed.)? I don't know if this is a disadvantage though. May5 comment What are the primary disadvantages of Dummit and Foote's abstract algebra text (3rd ed.)? It has almost no category theory. May5 comment Example of a monomorphism and epimorphism that is not isomorphism. I wouldn't call them exact duplicates May5 awarded Favorite Question May5 answered In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all element non zero in $A$ is invertible. May5 revised not sure how to do this edited tags May5 comment Let $f(x) = x^2 + x + 41$. Show that $f(n)$ is prime for $0 \le n \le 39$, but $f(40)$ is composite. No, because you didn't prove the induction can help you prove it for $n=5$ by assuming it is true for $n=1,2,3,4$. You only proved it when the assumption is that it is true for $n=1,2,3\dots 38$ and you want to prove it for $39$. So the induction never even starts. May5 comment Is the condition of PID necessary? I don't know, this is the proof I know, but I don't think you can prove it straight-forwardly. May5 answered Prove $A\cap (B-C) = (A\cap B) - (A\cap C)$ May5 comment Let $f(x) = x^2 + x + 41$. Show that $f(n)$ is prime for $0 \le n \le 39$, but $f(40)$ is composite. You didn't do your induction correctly. You have to prove that if a statement is true for all positive integers smaller than $n$ then it is also true for $n+1$. You just proved the particular case when $n$ is $39$. You have to prove it for arbitrary values of $n$ so that the induction works. Of course it is impossible to prove it for arbitrary values of $n$, since it is not true for all valuse of $n$. Induction is used to prove statements for all natural numbers, you only want to prove the statement for some values of $n$, this is why induction won't work. May5 comment Is the condition of PID necessary? Oh right, I remember my teacher did this a couple of weeks ago, but I wasn't paying much attention. Thank you very much, this process has been very profitable for myself also. May5 revised Is the condition of PID necessary? added 13 characters in body May5 comment show $p$ is divisible by $(x^2 +y^2 +1)$ lol${}{}{}{}{}{}$