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seen Dec 15 at 16:48

Nov
16
answered Probability of four-of-a-kind flawed logic
Nov
6
answered Isomorphism of quotient fields
Nov
2
comment How does $\in$ behave with simple algebra dealing with sub gradients?
What do you mean if a subset has a "related inverse"? Usually the sum of 2 subsets is defined as $A + B = \{ a+b : a \in A, b \in B\}$. With this definition, there is never an inverse of a subset that has more than one element. If for example $A = \{1,2\}$, then $B = \{-1, -2\}$ is not an inverse of $A$. The set $A+B$ contains the element 1 + (-2) = -1, so $A+B$ is not the identity element with respect to addition of subsets (which would be $\{0\}$.)
Nov
2
answered How does $\in$ behave with simple algebra dealing with sub gradients?
Oct
24
comment Intuitive Meaning of Quotient Ring
This "treating elements of $I$ as though it were zero" also explains why an ideal is defined the way it is: because 0+0=0 (hence $I$ should be closed under addition) and $a \cdot 0 = 0$ (hence $a \in R, x \in I$ should imply $ax \in I$).
Oct
23
answered How to find $α^2(β^4 +γ^4 +δ^4)+β^2(γ^4 +δ^4 +α^4)+γ^2(δ^4 +α^4 +β^4)+δ^2(α^4 +β^4 +γ^4)$
Oct
21
answered If $G$ is simple, then $\epsilon \leq {v \choose 2}$ - Bondy/Murty - Graph Theory with Applications Page 4
Oct
20
revised What to do with a random variable when we know its mean and variance but does not know which distribution it is?
edited tags
Oct
19
revised Disjoint open sets in $\mathbb{R}^N$
improve title
Oct
19
comment The set $\mathbb{Z}$ is totally ordered
It seems like the purpose of this exercise is to prove the trichotomy property.
Oct
19
comment A question on branch of an inverse
Yes, that is what I'm referring to.
Oct
19
answered A question on branch of an inverse
Oct
18
answered Marriage Market Proof (Alternative Proof of Rural Hospitals Theorem)
Oct
12
comment What is the dimension for this subspace?
In 2, we could have $x=0,y=1,z=-1$.
Oct
8
revised Proving $AAS \Rightarrow$ two triangles are congruent
added 369 characters in body
Oct
7
answered Proving $AAS \Rightarrow$ two triangles are congruent
Oct
6
comment Using FTC to calculate $\int_a^b \frac{1}{z} dz$
Yes, that is correct.
Oct
6
comment Using FTC to calculate $\int_a^b \frac{1}{z} dz$
The FTC works for any branch of the log function that doesn't intersect the curve of integration. The value of the integral doesn't depend on the choice of cut line as long as it doesn't intersect the curve of integration. So if there exists a cut line that intersects none of the sides of the triangle, then you get $\int_a^b + \int_b^c = \int_a^c$. The fact that some other cut line would intersect the triangle doesn't matter. You have to find a triangle where every cut line intersects at least one of the sides.
Oct
5
comment Using FTC to calculate $\int_a^b \frac{1}{z} dz$
For this triangle, it would be more convenient to choose the cut line as the positive real line (rather than using the principal branch), since the positive real line does not intersect any of the sides of the triangle. This gives a single branch of $\log$ that works for all 3 sides of the triangle, so it won't be a counterexample for the second part of the problem.
Oct
5
comment Misunderstanding in Cartan-Eilenberg?
If $I=(a)$ is a principal ideal, consider the map $\Gamma \to I$ sending $x \mapsto xa$.