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visits member for 4 years
seen Jul 22 at 10:08

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awarded  Yearling
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awarded  Yearling
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awarded  Nice Answer
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awarded  Good Answer
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awarded  Yearling
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awarded  Quorum
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awarded  Nice Answer
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comment Proof: Series converges $\implies $ the limit of the sequence is zero
You are mistakingly assuming that the sequence actually converges to something. The other proofs also show that the limit exist, AND it is 0.
Sep
11
comment Boy Born on a Tuesday - is it just a language trick?
@Gadi The formulation you give is indeed ambiguous: we do not know a probability model for who goes to open the door. The formulation in the original question is unambiguous and indeed is a simple problem of conditional probability.
Sep
11
comment Boy Born on a Tuesday - is it just a language trick?
@T. No, it is not. In the Monty Hall problem there is a random choice, and then the showman has to make a choice about which door to open (he certainly does not want to open the door with the goat). In this case, there is not a random choice, after which the parent has to reveal information (for instance a random question). It is just plain conditional probability: the fact that the parent reveals this piece of information has nothing to do with the fact that he/she could reveal another.
Sep
11
comment Boy Born on a Tuesday - is it just a language trick?
@Gadi: I do not agree. I think you are making confusion with similar sounding problems like the Monty Hall one. In this case there is a very precise information; there is no need to speculate why the parent gave this piece of information instead of another one. Of course he/she might have said other things, for instance "I have a boy which is not born on Sunday", and you would obtain a different question, but this does not affect our problem.
Sep
11
answered Can we define definitions as axioms in logic?
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comment Induction on Real Numbers
It seems to me that ii) is flawed. You could have $[0, x] = [0, y)$ (think of the case of natural numbers where y = x+1). Hence in your argument you cannot deduce that $y \notin S$.
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awarded  Scholar
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accepted CAS with a standard language
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awarded  Student
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asked CAS with a standard language
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comment How many ways to define sine and cosine?
Proving their properties from this definition (especially the periodicity) is a wonderful exercise in a first course on (qualitative study of) differential equations.
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awarded  Critic
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comment Good books and lecture notes about category theory.
Are you implying that usually books are not written by experts? :-?