True Definition of the Real Numbers
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True Definition of the Real Numbers

I've found lots of resources that say this is a real number if it's not rational, but what is a real number, really? I mean what is the definiti...

Published: Aug 24, 2026

Number of Ways to Draw a Pair in a Poker Deck
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Number of Ways to Draw a Pair in a Poker Deck

I am confused over calculating the number of ways in which I can select a pair out of a deck of 52 cards. This is how I go about solving the problem: Foll...

Published: Aug 24, 2026

Mathematical Operator to flip a vector
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Mathematical Operator to flip a vector

Is there a mathematical operator which flips a vector from left to right (or up to down). Say \begin{align} a = [1~ 2~ 3]\quad\text{and}\quad b = [3~ 2~ 1...

Published: Aug 24, 2026

Finding best response function
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Finding best response function

Consider two players Player 1 choose $x_1$ Player 2 choose $x_2$ $x_1, x_2 \in [0,b]$ and $b>0$ The payoffs for players 1 and 2 are identical and equal...

Published: Aug 24, 2026

Lambert W / Product log function?
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Lambert W / Product log function?

I would like to solve this equation: $$n \cdot 2^n = 15000$$ And according to WolframAlpha $$n=\frac{W(15000\log(2))}{\log(2)}, \text{ where }\log\text{ i...

Published: Aug 24, 2026

What does expected value of sum of two discrete random variables mean?
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What does expected value of sum of two discrete random variables mean?

I am confused with summing two random variables. Suppose $X$ and $Y$ are two random variables denoting how much is gained from each two games. If two game...

Published: Aug 24, 2026

Taylor series third order approximation
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Taylor series third order approximation

There has been this question that had been bothering me for a while and I could not find a satisfying answer on the internet or any of the books even thou...

Published: Aug 24, 2026

Even Digit Series (2,4,6,8,20,....) [duplicate]
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Even Digit Series (2,4,6,8,20,....) [duplicate]

I have a series of numbers whose Nth term is a number whose all of the digits are even. The series is of course divergent , but i am interested in finding...

Published: Aug 24, 2026

Calculating an Ellipse given the Orbital Eccentricity and a Vertex?
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Calculating an Ellipse given the Orbital Eccentricity and a Vertex?

I know that the formula for Eccentricity is e = c/a where c is the distance from the center to a focus and a is the distance from that focus to a vertex. ...

Published: Aug 24, 2026

Lie algebra of Lorentz Group $O(1,3)$
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Lie algebra of Lorentz Group $O(1,3)$

Let $$ O(1,3)=\{A\in GL_4(\mathbb R):A^TgA=g\} $$ where $g$ is the diagonal matrix with $1$ on the first diagonal entry, and $-1$ on the other diagonal en...

Published: Aug 24, 2026

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