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Jun
28
comment How to define the disciplines of mathematics
Everything is both similar and different from everything else. The general ideas of the above three categories solidify around their respective centers, but they cross over quite a bit.
Jun
6
comment 'Obvious' theorems that are actually false
For #4, the restriction where this _does work are given by the Fubini-Tonelli theorem
Jun
6
comment Why does differentiating a polynomial reduce its degree by $1$?
Nice... this is Sturm's theorem
Jun
6
comment Generalised Binomial Theorem Intuition
"why don't they teach it in secondary school?" - That's what math.SE is for.
Apr
10
comment (k+1)th, (k+1)st, k-th+1, or k+1?
Also, the ordinal for 301 is pronounced "three hundred and first".
Mar
27
comment Why use *λx.x* instead of *f(x)*?
One could also ask then why don't we use '(x)f' instead of 'f(x)' (postpositioning the function name makes it easier to interpret composition of functions in a left to right reading.
Mar
7
comment What is exponentiation?
It all depends on what you mean by 'mean'. If it is simply a matter of "I don't get it" despite being able to do the manipulations, one could say that there is no intention of you to 'get it', it just a mindless preservation of the rules for basic exponentiation (which I think you do 'get') to allow some calculation. If 'mean' means "I don't see a quick generalization that encompasses integers and reals" then the best generalization is to complex numbers and scaling rotation. (hmm, that doesn't explain it for reals though...OK stick with the calculus/derivative equals itself.)
Mar
5
comment Does there exist a system such that the additive identity is non-zero?
In the semiring of languages (sets of strings), union of two languages acts like addition, and the additive identity is the empty set. Multiplication is string concatenation (well a little more complicated than just that) and the multiplicative identity is the empty string.
Mar
5
comment Does there exist a system such that the additive identity is non-zero?
@Brilland: they might be tempted to call it that, but that would be misleading about the meaning of the operators. The abstract operator '⊗' acts like multiplication. The fact that it is implemented as arithmetic addition is, well not exactly irrelevant, but just not as important is the fact that it acts analogously to arithmetic multiplication.
Feb
9
comment combinations $\sum_{k=1}^m kn_k=m!$
Just to be clear, for example, if $m = 4$ you'd like the number of solutions of $24 = n_1 + 2 n_2 + 3 n_3 + 4 n_4$ ?
Feb
8
comment combinations $\sum_{k=1}^m kn_k=m!$
So, to put into words, you're trying to find the integer partitions of $m!$ into $m$ parts?
Feb
8
comment Find “n” using the following conditions.
My bad...I missed the '$P(x)$ is a polynomial of degree $3n$'
Feb
8
comment combinations $\sum_{k=1}^m kn_k=m!$
What is $n_k$? That's not a notation I'm familiar with if it is some function of $n$ and $k$.
Feb
8
comment Find “n” using the following conditions.
This doesn't seem possible. It looks like $P(k+3) = P(k)$, so $P(3n+1) = P(3n-2) = 1$ which is inconsistent with $P(3n+1) = 730$.
Jan
28
comment The Hexagonal Property of Pascal's Triangle
I haven't been ignoring you. I'm still thinking about all this.
Jan
26
comment We are learning about LU Decomposition .. because?
What can you use LU decomposition for? (solving a system of equations) Why can't you just invert the matrix and multiply on the other side? (you certainly can but it takes longer). Also you can do LU decomposition in-place. Which is what Amzoti's link says.
Jan
4
comment ordering 3 couples in 3 rows
Is it three friends or six?
Dec
30
comment Bijection from ordered pairs of $[0,n]$
What's wrong with the Cantor pairing function? The bijection is infinite.
Dec
30
comment How to find coefficient of $x^8$ in $\frac{1}{(x+3)(x-2)^2}$
I think the OP wants a rational, not a floating point number.
Dec
26
comment General form for the series expansion of $e$
Does this mean that $$\sum_{n=1}^{\infty} \frac{n^k}{n!} = e \cdot B(k)$$ where B(k) is the number of set partitions of $k$?