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1d
comment Mutual exclusive events are dependent
Nothing can be concluded from this if $A$ and $B$ both have probability $0.$ More information is needed.
2d
comment Mutual exclusive events are dependent
Do you know anything else about the probability space? In particular, is it possible that $P(C)=0$ for some $C\ne\emptyset$?
2d
answered Prove: If $A \subset B$ then $P(A) \le P(B)$ and $P(B-A) = P(B)-P(A)$
Feb
4
comment Complex Numbers in Factoring
What about $-x^2-9$?
Feb
4
comment Proving a topology is not induced by a metric
See here.
Feb
4
comment Quotient of maximal and prime ideals
You need to know a bit more about $I$ and $J$ if $I/J$ is to make sense, I think. However, if it does make sense, there is an isomorphism theorem that $R/I\cong(R/J)/(I/J).$ From there, you can use the quotient characterizations of maximal/prime ideal.
Feb
3
comment Proving continuity with epsilon delta
@user21820: Personally, I prefer "Take an arbitrary $\epsilon>0.$" I was just illustrating a more appropriate word than "random."
Feb
3
comment Proving continuity with epsilon delta
You can also say "Let $\epsilon>0$ be arbitrary."
Feb
3
comment Do we have $\frac{1}{a} - \frac{1}{b} = b - a$?
I also found an error in my answer. It's fixed now.
Feb
3
revised Do we have $\frac{1}{a} - \frac{1}{b} = b - a$?
added 271 characters in body
Feb
3
answered Do we have $\frac{1}{a} - \frac{1}{b} = b - a$?
Feb
3
answered Can this Boolean expression be simplified any further using the commutative law?
Feb
3
answered Prove that if $n$ is odd, then $-n$ is odd.
Feb
2
revised Prove that $\dim(U+W) + \dim(U\cap W) = \dim U + \dim W$
edited tags
Feb
2
comment Cantor Diagonal Argument with complete list of reals
Related.
Feb
2
comment Can a diagonal be longer than the list being diagonalized?
If $n$ is a cardinal variable, then we can sensibly say things like "$n\to\aleph_0$" or "$n=\aleph_0.$" If $n$ is a real variable, then we can sensibly say "$n\to\infty,$" but we cannot sensibly say "$n=\infty.$"
Feb
2
comment Can a diagonal be longer than the list being diagonalized?
@Carl: Not at all; rather, I disagree with Watkins' misleading characterization of Cantor's work. There are many different infinite cardinalities, as Cantor showed, but cardinal numbers and real numbers are not the same thing. Finite cardinal numbers behave in the same way as real numbers, as far as their respective addition and multiplication operations are concerned; this does not extend to subtraction and division, though, so we can't treat finite cardinals as real, either. Trying to treat cardinal numbers like real numbers will only confuse you further.
Feb
2
comment Cantor Diagonal Argument with complete list of reals
+1: I wholeheartedly agree! A direct proof-schema is much less confusing.
Feb
2
comment Can a diagonal be longer than the list being diagonalized?
Here's your error: "$d_\infty=n_{\infty,\infty}.$" Stop trying to treat "$\infty$" like a real number. It is merely a symbolic representation of growth without bound. That is, the natural numbers grow forever; they never actually "reach" anything we could describe as infinite.
Feb
1
comment Set Theory and $1 = 0.999\dots$
@Carl: It will never fall short. When she reaches the $n$th tree, she finds that it has $n$ branches, as desired. On the other hand, she will never finish the process, since there is no last tree on the street; however, if we choose any tree on the street, there are only finitely-many trees before it, so we can be confident she will reach the chosen tree, given enough time.