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seen Jul 4 at 23:58

Jul
22
comment Why isn't reflexivity redundant in the definition of equivalence relation?
Not to sound as though I'm picking on you, but I think this revised claim is also false. My first clue was the fact that the wikipedia article you referenced said that Euclidean+Reflexive => Equivalence. Since being reflexive is a stronger requirement than being serial I sought a counterexample, the smallest of which I can find is on the set {1,2} and is defined as Rxy <-> y = 2.
Jul
22
awarded  Nice Question
Jul
22
comment Why does the series $\sum_{n=1}^\infty\frac1n$ not converge?
Thank you for adding this answer. I was hoping to avoid an answer that involved integration, so I also prefer AgCl's answer. But I am happy to see more than one demonstration/proof.
Jul
22
comment Why is $x^0 = 1$ except when $x = 0$?
Unfortunately there's also a debate about whether 0 is a natural number (see math.stackexchange.com/questions/283/is-0-a-natural-number). But I'll take your usage to mean 'nonnegative integer', and that you're voting for $0^0 = 1$.
Jul
22
comment What is the meaning of this symbol ($\models$)?
Sorry, I realise that I haven't actually answered your question (about the meaning). I've seen it used in logic to stand for semantic entailment, but I imagine it has other uses.
Jul
22
answered What is the meaning of this symbol ($\models$)?
Jul
22
awarded  Commentator
Jul
22
comment Why is $x^0 = 1$ except when $x = 0$?
@Neil, except that 0^x = 0 is not true for all non-zero x (e.g. x = -1).
Jul
22
comment Why isn't reflexivity redundant in the definition of equivalence relation?
Perhaps I made up the noun form. If you google 'serial binary relation' it will come up. Although if you google 'seriality of binary relations' it will come up there too.
Jul
22
comment Why isn't reflexivity redundant in the definition of equivalence relation?
This seems to fail though because (as Akhil mentioned) the empty relation would satisfy this but it's not reflexive.
Jul
22
comment Are there any interesting semigroups that aren't monoids?
I'll try my luck. If the community decides to close the question on grounds of arcaneness then so be it.
Jul
22
answered In how many different ways can I sort balls of two different colors
Jul
22
comment Are there any interesting semigroups that aren't monoids?
Yes, I realise that it's subjective what counts as 'interesting' but hopefully potentially answerers can cope with this.
Jul
22
asked Are there any interesting semigroups that aren't monoids?
Jul
22
answered Why isn't reflexivity redundant in the definition of equivalence relation?
Jul
22
comment Is $.999999999… = 1$?
This proof also relies on the assumption that every real number can be represented by a (potentially infinite) decimal, which might or might not be accepted by someone asking the original question.
Jul
21
comment Why is $x^0 = 1$ except when $x = 0$?
The first line here seems false, since if x = -1, we get 0^(-1) which is also undefined. So at best we have 0^x = 0 for x>0.
Jul
21
awarded  Scholar
Jul
21
accepted Why does the series $\sum_{n=1}^\infty\frac1n$ not converge?
Jul
21
awarded  Teacher