# caya

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bio website location Sydney, Australia age 48 member for 1 year, 9 months seen 5 hours ago profile views 20

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 2d comment How does exponentiation relate to multiplication? You need to prove that $ln(x~y) = ln(x) + ln(y)$, which follows from the definition by a change of variable. Then it should not be hard as $e^x$ is defined by the inverse (in your text). Aug14 comment Determinant of a matrix with $t$ in all off-diagonal entries. So, there is a typo in the post... Aug14 comment Determinant of a matrix with $t$ in all off-diagonal entries. When $n=2$ seems to fail. $1-t^2$ RHS, $-2 t^3-3 t^2+1$ LHS, right? Aug12 comment Formal Proof that area of a rectangle is $ab$ What I like about the question and the answer is that it shows that not everything in maths is proving: a good part of any real maths involves finding the right axioms that are useful to the problem at hand (+1 to both) Jul30 comment What is $\displaystyle\lim_{h\to 0}\ h\left(\sum\limits_{n=1}^\infty{n}\right)$? A believe this question illustrates that for limits to be interchangeable, they both need to exist. Although the above does not exists, $\sum\limits_{n=1}^\infty{\left(\displaystyle\lim_{h\to 0}\ h~n\right)}$ does. Jul23 comment A set of all rational numbers in $[0, 1]$? And a set is dense in other (in topology), when its closure is the whole enclosing set. It is mentioned in wikipedia too. Jul23 comment A set of all rational numbers in $[0, 1]$? $\bar{A}$ is the closure operation: adding all limiting points to a set in the topological sense. Some texts use $Cl(A)$ instead, like in wikipedia: en.wikipedia.org/wiki/Closure_(topology). See the link :) Jul23 suggested suggested edit on A set of all rational numbers in $[0, 1]$? Jul23 answered A set of all rational numbers in $[0, 1]$? Jun13 comment Is this question too easy or am I getting it wrong? If I remember correctly (in Spivak's) $e^x$ is defined through its Taylor series and proved continuous that way. Jun12 comment Is this question too easy or am I getting it wrong? Attention readers: this is the answer! The one flagged by the PO is a circular definition. Jun12 answered Mathematics textbooks with history and/or motivation? Jun6 answered What jobs in Mathematics are always in demand, and are deeply Mathematically specialised or greatly general? Jun2 comment Identification of a curious function @Yuval, I saw something similar when reviewing election strategies (as in Politics) in an election where people vote for a list of candidates, there is a number of places to be elected $N$ (say a senate), and lists get as many places as percentage votes won: $places = floor(N P_l)$. The tricky part was that there is a remanent after allocating all lists, as one cannot allocate a fraction of a place, an allocation then was from greatest residual to lowest. So, what's the best strategy, split the party in many lists or nominate a single one? Plotting, we arrive at something similar. May29 revised Why is it that $\int_a^b \int_c^d f(x)g(y)\,dy\,dx=\int_a^b f(x)\,dx \int_c^d g(y)\,dy$? added 29 characters in body May29 revised Why is it that $\int_a^b \int_c^d f(x)g(y)\,dy\,dx=\int_a^b f(x)\,dx \int_c^d g(y)\,dy$? added 2 characters in body May29 revised Why is it that $\int_a^b \int_c^d f(x)g(y)\,dy\,dx=\int_a^b f(x)\,dx \int_c^d g(y)\,dy$? added 2 characters in body May29 answered Why is it that $\int_a^b \int_c^d f(x)g(y)\,dy\,dx=\int_a^b f(x)\,dx \int_c^d g(y)\,dy$? May29 comment Logic and mathematical variables as objects Also, the concept of valuation is from model theory. But it seems you want to "internalise" valuation for the variable type. So, sorry about the confusion; although you will need some sort of semantic for your logic anyway... May28 comment Logic and mathematical variables as objects @Angelorf, I updated my pseudo-answer; good luck!