Mitch
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 Jul2 awarded Curious Jun28 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. Jun6 comment 'Obvious' theorems that are actually false For #4, the restriction where this _does work are given by the Fubini-Tonelli theorem Jun6 comment Why does differentiating a polynomial reduce its degree by $1$? Nice... this is Sturm's theorem Jun6 comment Generalised Binomial Theorem Intuition "why don't they teach it in secondary school?" - That's what math.SE is for. Apr10 comment (k+1)th, (k+1)st, k-th+1, or k+1? Also, the ordinal for 301 is pronounced "three hundred and first". Apr8 awarded Nice Answer Mar27 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. Mar21 awarded Nice Question Mar7 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.) Mar5 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. Mar5 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. Feb17 reviewed Approve unlimited combination Feb15 answered What's the intuition behind Pythagoras' theorem? Feb9 reviewed Approve Find angle between two planes Feb9 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 $24 = n_1 + 2 n_2 + 3 n_3 + 4 n_4$ ? Feb8 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? Feb8 comment Find “n” using the following conditions. My bad...I missed the '$P(x)$ is a polynomial of degree $3n$' Feb8 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 $k$. Feb8 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 $P(3n+1) = 730$.