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comment A sheet of cardboard measures 15cm by 7cm. Four equal squares are cut out of the corners and the sides are turned up to form an open box.
"Algebraic geometry" doesn't mean solving geometry problems with the help of algebra. If anything, it's the other way around.
Jul
29
comment Proofs needed for observations regarding prime-partitionable numbers.
This is unnecessarily hard to parse. Are all the subscripts needed; can't you just use $p$ and $q$ and $k$, for instance? The recent edit changed "pp" to $p^2$, is that right? What does $\#k_{1a}$ refer to, and what does "the $p_{1b}$ are distinct" mean?
Jul
14
comment Can I have a logical explanation for why this number is so ridiculously close to a whole number?
It's more impressive that it's very close to a whole number that is very close to a perfect cube.
Jul
13
answered An “apparent” contradiction for eigenvalues signs of $A=\left( \begin{array}{cc} a & -a \\ a-1 & 1-a \\ \end{array} \right)$.
Jul
9
comment Is it possible to have random number chain relation?
You're adding a bunch of stuff to $I$ to get $38$, and subtracting the same bunch of stuff from $I$ to get $2$. That is, $I+x=38$ and $I-x=2$, where $x=5+7+2+4$ (the sum of your four random numbers). From this you can deduce that $I=20$ and that $x=18$, but that's it... there's no way to break $x$ back into its components.
Jul
9
revised Is it possible to have random number chain relation?
deleted 3 characters in body
Jul
7
comment Does the Russell Set exist?
If you have a predicate $\phi(x)$ that is true or false for every set, then $\{x : \phi(x) \}$ is a class (and may or may not also be a set). The "universal set" (really, a proper class) comes from letting $\phi(x)$ be true for all $x$. There's really no question as to whether a class "exists"... if $\phi(x)$ is a well-formed formula in the language of set theory, then the associated class is meaningful, and moreover can be intersected with sets to yield sets.
Jul
7
revised Another kind of derangement?
added 494 characters in body
Jul
7
answered Another kind of derangement?
Jul
7
comment Another kind of derangement?
Agreed. If the first reading is correct, then it's irrelevant how big the teams are... that's the only reason I think the second reading may be intended. But OP is going to have to weigh in.
Jul
7
comment Another kind of derangement?
I think it's supposed to be hard, so the second reading is the correct one :).
Jul
7
comment Another kind of derangement?
The phrasing isn't entirely clear, but I think you mean, assign three staff members to each head so that no staff member stays with the head he had previously?
Jul
6
awarded  Good Answer
Jul
5
comment Density of probability in a square
If $X$ and $Y$ are uniformly distributed over $[0,1]$, and independent, then their joint density is just $f(x,y)=1$.... not $f(x,y)=1/(xy)$.
Jul
2
comment Inclusion-exclusion-like fractional sum is positive?
I see! So if you have $n$ sets you have to carry out the sum to the $n$-th term.
Jul
2
answered Inclusion-exclusion-like fractional sum is positive?
Jul
2
answered proof by contradiction puzzle
Jul
1
comment prove that this number contains two equal digits
Two things to check. First, that this operation conserves some invariant about the number. Second, that $7^{1996}$ has a different value of this invariant than all $10$-digit numbers with no repeated digits. @RobertIsrael's suggestion was that you use "is it divisible by 9?" as the invariant.
Jul
1
answered Number of ways through a modified grid
Jun
30
awarded  elementary-number-theory