I am trying to understand the significance of Cantor's diagonal argument. Here are 2 questions just to give an example of my confusion. From what I understand so far about the diagonal argument, it finds a real number that cannot be listed in any nth row, as n (from the set of natural numbers) goes to infinity. It does this by listing real numbers and making a rule that its nth column cannot have a digit in the corresponding nth row. This produces a real number that cannot be listed... Read more ..read more

HI all !!!! If someone can help would be great I am a fairly new seller on amazon, i want to apply a Target Costing approach to my product i will source. I am planning to sell Item X for £9.99, + Amazon Fees(£5.64). How do i calculate Targets cost, to achieved a 25% Margin ..read more

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An ellipse is a conic section, i.e. it can be described as the surface of a cut through a cone. Given an ellipse, I want to calulate the properties of its corresponding cone and how it was cut out of it. I might later follow up with more questions about the relationship of an ellipse to a cone, but here we start: - The end points of the major axis of the ellipse are points on the cone's surface (mantle) at different heights. What is the (circular) diameter of the cone at each of those two... Read more ..read more

The question states to simplify the expression, I thought I understood canceling common factors but I don’t understand why you would cancel both 4s on one side of the division sign. I’m completely lost at this point. Wouldn’t canceling 4x4 cancel out the -16 and and make it -1? I get 60 ..read more

Hi guys could you help me with these questions please ? r<=k<=n, S(n,k)^{r} How I can find the number of partitions of a set {1...n} Into k blocks such that the elements {1...r} must be in different blocks ? How I can find the recurrence relation ? Thanks ..read more

A triangle as an example the bisector not through the center of figure plane. I'm interesting on trapezoid. We know that by Intermediate value theorem guarantee that there is infinite line can divide trapezoid to be two equal area. I confused the properties and how to generalization ensure that the line will divide trapezoid be two equal area ..read more

Toss a fair coin for 5 times. Describe the sample space [imath]\Omega.[/imath] We want to consider functions [imath]X : \omega \rightarrow \{-1,1\}.[/imath] Now describe the probability space [imath]( \Omega, \mathcal{F}_2, \mathbb{P}_2) [/imath] that arises if we want that only combinations of sets of the type [imath]A_i = \{ \omega \in \Omega :\text{ Number of heads} = i\}, i =\{ 0,1,2, 3,4,5 \}[/imath] should be events. How many [imath]\mathcal{F}_2 [/imath] measurable functions X with [imath]\mathbb{E}[X]=0 [/imath] are there? My... Read more ..read more

if [(sinx)^4]/2 + [(cosx)^4]/3 = 1/5 then prove that (tanx)^2=2/3 I tried solving this as follows taking LCM as 6 {3[(sinx)^4] + 2[(cosx)^4]}/6=1/5 {3[(sinx)^4] + 2[(cosx)^4]}=6/5 now using sin^n+cos^n=1 property (sinx)^4 + 2=6/5 (sinx)^4=-4/5 but -ve should not come there as sin is raised to 4th power what I did wrong ..read more

Hello everyone, I am considering how I could use General Additive Mixed Models (in R) to validate the effect of categorical variables (C, V, syllable, etc.) on my data. The problem is that my continuous variable is a series of values that form a trajectory. I would like to find a statistical way to capture difference in both trajectory height and trajectory shape. Here is a small sample of my data: dput(df) structure(list(syllabe = c("CV", "CV", "VCs", "CV", "CV", "CVs", "CV", "CV"... Read more ..read more