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Jun
19
answered If a functor $\varphi : C \to C'$ is full, then so is the functor $\varphi \circ$
Jun
16
comment Ring localization and ideals
The set of all elements of $A_S$ of the form $i(a)$ comprise a representation of $A$ in $A_S$. You have, for instance, $\mathbb Z$ in $\mathbb Q$, and of course $\mathbb Q$ has many non-integers. (The example is misleading in that $i$ is injective in that case, which is not always true).
Jun
8
awarded  Strunk & White
Jun
8
revised If $\alpha$ is a root of $f(t) = t^n + a_{n-1}t^{n-1} + \cdots + a_0$, then $|\alpha| \leq n \max_i |a_i|$
added 1 character in body
Jun
5
comment About the Heine-Cantor theorem.
Clearly from the graph...
May
14
comment Let $(X, \mathfrak T)$ be a topological space and suppose that $A$ is a subset of $X$. Then $A'$ is a closed set.
Have you carefully proven that if $A=\mathbb Q$, then no rational number belongs to $A'$? (You're right that the set of irrationals is neither open nor closed)
May
4
comment Simplifying an function with complex numbers
Wait, so you know in advance that both sides are real numbers?
May
4
comment Polynomials of degree less than $n$ that agree at $n$ values
Technically, yeah it is due to the definition of polynomial (over a field), but there is at least one major creative step along the way.
Apr
24
revised Chinese Remainder Theorem - solving a modulo with big numbers
deleted 8 characters in body
Apr
24
comment Chinese Remainder Theorem - solving a modulo with big numbers
I'm stuck under a tree trunk! @Somebody please help!
Mar
21
awarded  Yearling
Dec
21
awarded  Constituent
Dec
9
awarded  Caucus
Dec
3
comment Nobody told me that self teaching could be so damaging…
I get the sense that you feel you know every aspect of the subjects you are taking. There is absolutely no way that is true; you simply haven't looked hard enough to find the interesting stuff. Often times the book will have exercises geared toward the more advanced reader at the end of its exercise sets, see if that is true for your textbooks. Also, look for patterns in your problems sets or see if there is some abstract result that solves your problems more efficiently or gives you deeper understanding of the answers.
Dec
2
comment Determine $\phi(2^{399}+1)$
My crystal ball works!
Nov
14
comment Determine $\phi(2^{399}+1)$
Intended answer: some very large number.
Oct
19
comment xy+x+y=0 What is the inverse Element?
@Clayton Your confusion arises from mixing up the two multiplication operations.
Sep
30
awarded  Explainer
Sep
24
awarded  Autobiographer
Sep
4
comment Bisectors problem
So it is just a hypothesis that N exists and B lies between M and N?