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 Yearling
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Aug
23
comment Motivation for different mathematics foundations
"One of the problems of second-order logic is that it has no proof verification algorithm that we can run a computer program to determine the validity of a proof" - holy shit, what? I thought second-order logic just sacrificed completeness.
Aug
22
awarded  Yearling
Jul
7
comment G/N read as G modulo N.
Man, I hate this terminology. It's like calling $6/3$ both "6 mod 3" and "6 divided by 3".
Jul
4
comment Completion of the real numbers
@MartianInvader: But that's not an embedding, is it? In any case, the metric induced by such an injection certainly doesn't induce the standard topology of $\mathbb R$.
Jul
3
comment How to prove the non-existence of a polynomial series that uniformly converges to this function?
"all polynomials are bounded" - uh, what?
Jul
2
comment Completion of the real numbers
How do you do the figure-eight or the circle with a line segment attached? I can see a continuous injection, but not an embedding.
Jun
22
answered Distributive property on fractions
Jun
14
comment When does convergence of subsequences implies convergence of sequence?
The question says that the shifted subsequences all have to converge to $l$. It doesn't look like they do in this example.
Jun
2
comment If an abelian group has more than 3 elements of order 2 then it must have at least 7 elements with order 2.
"I know that if a group is cyclic then it has exactly 1 element of order 2." - it can also have none.
May
26
comment How to quantify the differencen between 2/4 and 20/40?
It's worth specifically emphasizing that the reliability in this answer is not the reliability of the prediction methods - it's how reliably we know the reliability of the prediction methods. The lower variance in the second case doesn't tell us anything about which predictor is better.
May
23
comment why is $2.2250738585072014\text{e}{-308}$ not a number?
"It's just that, in order to properly store this number, the calculator will need a fair bit of memory to store it accurately, and you've essentially attempted to exhaust it." - this isn't an accurate description of what's going on. The problem has nothing to do with memory limitations; it's an issue of what numbers are representable in the calculator's floating-point format, and possibly also an issue of what exactly the OP typed (since NaN is a rather unexpected error result - I'd expect something like 0 or an underflow message).
May
23
comment $\frac{1}{2}\int\frac{1}{1-x^2}d(1-x^2)$
While it's possible that the given answer is wrong, it's also possible that there's some context we're not seeing that restricts the domain of the function to $|x|<1$.
May
17
comment Are there mathematical objects that have been proved to exist but cannot be described in words?
Every time questions like this come up, people immediately diagonalize over sentences of the language to conclude there are countably many definable objects, and it's impossible to get them to stop. If ZFC is consistent, then there must be models of ZFC where everything in the model actually is definable, even though it seems like there should only be countably many definable objects. Please read Joel David Hamkins's more detailed answer on MathOverflow.
May
17
comment Are there mathematical objects that have been proved to exist but cannot be described in words?
We can't say that there are countably many definable objects, because we can't actually construct the correspondence between a definition and the object it defines. If we could, we could do things like define the lowest undefinable ordinal. See Joel David Hamkins's more detailed answer on MathOverflow.
May
11
comment Why are two planes parallel to the same line not necessarily parallel?
@Ant: Sure, but given any line, there are infinite lines parallel to that line too, and yet parallelness is transitive for lines.
May
10
comment Math problems that are impossible to solve
No, seriously. As you've stated it, the problem is decidable. The set of Wang tiles has to be an input, not hardcoded into the problem, for the problem to be undecidable.
May
10
comment Math problems that are impossible to solve
I think you might want to reword this. The way you've written it, an algorithm to solve that problem would just be "return True" or "return False", since it only has to work for one specific set of tiles.
May
9
comment Is there any way to define arithmetical multiplication as other thing than repeated addition?
The cartesian product-based definition doesn't involve addition. You can compute the value by adding together how many times each first element appears, but you don't need to do it that way, and the definition doesn't say anything about how to compute the value.
May
9
comment Is there any way to define arithmetical multiplication as other thing than repeated addition?
It's easily possible to build from the axioms of set theory up to the definition of the product of naturals as the cardinality of the cartesian product without ever passing through the concept of addition.
May
6
comment Finding the angle between two line equations
@Mirko: Here's a picture of two lines intersecting: X As you can see, they form more than one angle. You've found the size of the big angles; 59 degrees is the size of one of the little ones.