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revised Question regarding cartesian product
edited body
Aug
22
comment Question regarding cartesian product
Welcome to Math.SE! What are your thoughts on the problem so far? What have you tried? The more we know about your efforts and thinking, the easier it will be for us to help you (and the more likely it will be that people will want to help you).
Aug
22
revised Question regarding cartesian product
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Aug
16
answered Find partial sums of the series $12+105+1008+10011+\dots$
Aug
8
comment what's the difference between isomorphism and homeomorphism?
My apologies! I actually meant to type "homomorphism," but that is nonsensical. In addition, I've discovered that I was incorrect in my impression that a monic epic morphism is always an isomorphism. My thanks for teaching me something new! (+1)
Aug
7
answered Error in proving of the formula the sum of squares
Aug
6
comment what's the difference between isomorphism and homeomorphism?
Well, what is a topological homomorphism? If it is a continuous function, then you're correct about the distinction between algebraic and topological morphisms. If it is a continuous (relatively) open map, then a bijective homomorphism is still an isomorphism.
Aug
6
awarded  Nice Answer
Aug
2
answered Find all whole numbers such that the number increased by the sum of its digits equals 73.
Jul
31
comment Show that the set of all finite subsets of $\mathbb{N}$ is countable.
@Mark: Not that it's probably relevant to the OP, but a countable union of finite sets needn't be countable in general without sufficient Choice. Here, of course, we're dealing with well-ordered finite sets, so it works out.
Jul
23
revised Are there real-life relations which are symmetric and reflexive but not transitive?
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Jul
19
revised How can I show that the closure of the set $\Phi = \{1, 2, 3, 4,\ldots\}$ is the set itself?
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Jul
7
comment Alternatives to quotient rule
Oops! That's what I get for trying to do this while half-asleep. That should be $$\frac{5x-5a+5a^2x-5ax^2}{(1+x^2)(1+a^2)(x-a)},$$ instead.
Jul
7
comment Alternatives to quotient rule
You're almost there in your second-to-last step! Instead, rearrange it as $$\frac{5x-5a+5a^2x-5ax^2}{x-a},$$ and try factoring the top by grouping from there. See if that gets you the rest of the way, but let me know if you get stuck again.
Jul
7
revised Alternatives to quotient rule
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Jul
7
answered Alternatives to quotient rule
Jul
6
comment My proof is wrong, can anyone tell me why?
Oliver: I believe what @André is trying to say is that we must restrict which pairs of integers we're looking at. In particular, we need to look at $x,y\in\Bbb Z$ such that $x+y\neq-1.$ Given that restriction, we will have $x(x+1)=y(y+1)$ if and only if $x=y.$
Jul
6
revised My proof is wrong, can anyone tell me why?
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Jul
6
comment My proof is wrong, can anyone tell me why?
If you want to disprove a universal statement, then all you have to do is find one counterexample. If you wish to disprove the universal statement $$\forall x\in\Bbb Z,\forall y\in\Bbb Z,[x^2-y^2=0]\iff[x-y=0],$$ for example, then you need to find some $x,y\in\Bbb Z$ for which the biconditional $$[x^2-y^2=0]\iff[x-y=0]$$ does not hold. One of the conditionals will always hold, so you'd need to find $x,y\in\Bbb Z$ such that $x^2-y^2=0$ and $x-y\neq0.$
Jul
6
revised My proof is wrong, can anyone tell me why?
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