## Upgrading to LaTeX For Mathematical Posts

This past week I spent roughly 10 hours learning LaTeX. I figured if I was actually going to use it to the full extent it should be merited I'd share

## Hume: The Essential Philosophical Works | Part II - A Treatise of Human Nature | Book 1 - Of Understanding | Part 1 - Of Ideas, Their Origin, Composition, Connexion, Abstraction, etc. | Section 1 - Of the Origin of Our Ideas | pp. 9 - 14

Pre-Reflection First off what even is a treatise? A treatise is a systematic, written argument using methodical discussion(s) of the facts, the principles involved, and the conclusions reached. Just wanted

## Hume: The Essential Philosophical Works | Part I - Prologue

Over the course of my lifetime I have garnered quite a collection of literature spanning the tedious to the abstract. From discussions on what is existence to specific supreme court

## Life Has Intrinsic Value: A Graphic Proposition

A little over a month ago I was pressed to prove or justify why I believed life has intrinsic value (valuable in itself, for its own sake). With this article

## The Rubin Report: Liberal or Not?

I'm writing this article actually rather late in comparison to the story, but oh well! So WHAT IS THE STORY ... Dave Rubin and his show the Rubin Report are

## Integral of cos(ln(x)) dx: A Third Method Via Euler's Identity

\begin{align*} & \int \cos \left( \ln (x) \right) \: dx = \dfrac{x}{2} \left( \cos \left( \ln (x) \right) + \sin \left( \ln (x) \right) \right) + C \\& \\& {\rm{Proof}}:

## Ramanujan's Beautiful Master Formula: Integral From 0 to ∞ (e)^(-x^n)sin(x^n) dx

\begin{align*} & f(x)=\sum_{n=0}^{\infty} \phi(n) \dfrac{(-x)^n}{n!} \LongrightarrowM \left[ f(s) \right] = \int_0^{\infty} x^{s-1}f(x) dx = \Gamma(s) \phi(-s) \\& \\& \therefore \int_0^ {\infty} e^{{-x}^n} \sin (x^n) dx = \dfrac{\left( \dfrac{1}{n} \right)! \sin

## Political Opinions: My Honest Answers

Prelude I am taking this test on 10/19/19. Result: QnA If economic globalisation is inevitable, it should primarily serve humanity rather than the interests of trans-national corporations.Agree***; would rather it

## Integral from 0 to 1 (ln(1/x))^b dx

\begin{align*} & \int_0^1 \ln^b{(x)} dx = (-1)^b (b)! \\& \\& {\rm{Proof}}: \\& \\& \therefore x=e^u \Longrightarrow \int_{-\infty}^0 u^b e^u du \\& \\& \therefore u=-g \Longrightarrow (-1)^b \int_0^{\infty} g^b e^{-g} dg

## Integral from 0 to 1 ln(x)ln(1-x) dx

BPRP achieved this result using power series. Today I will solve it using the Bose Integral. \begin{align*}& \int_0^1 \ln{(x)}\ln{(1-x)} dx = 2 - \dfrac{\pi^2}{6} \\& \\& {\rm{Proof}}: \\& \\& \therefore

## Integral from 0 to ∞ [x^a/(x^b+1)] dx

\begin{align*}& I(a, b) = \int_0^\infty \dfrac{x^a}{x^b+1} dx =\dfrac{\beta(\dfrac{a+1}{b}, 1-\dfrac{a+1}{b})}{b} \\& \\& {\rm{Proof}}: \\& \\& \therefore u=x^b \Longrightarrow \int_0^\infty \dfrac{u^{\frac{a-b+1}{b}}}{b(u+1)} du \\& \\& \therefore \int_0^\infty \dfrac{u^{\frac{a-b+1}{b}}}{b(u+1)} du = \dfrac{\beta(\dfrac{a+1}{b}, 1-\dfrac{a+1}{b})}{b} \\&

## Feynman's Trick: Integral from 0 to ∞ [(e^(-x)-e^(-bx))/x] dx

\begin{align*}& I(b) = \int_0^\infty \dfrac{e^{-x}-e^{-bx}}{x} dx = \ln{(b)}\\& \\& {\rm{Proof}}: \\& \\& I'(b) = \int_0^\infty e^{-bx} dx = \dfrac{1}{b} \\& \\& \therefore I(b) = \ln{(b)} + C \\& \\& \therefore

## Integral from 0 to 1 [ln(x)/(x-1)] dx

BPRP solved this integral using power series back in 2017. Today I will solve it using the Bose Integral. \begin{align*}& \int_0^1 \dfrac{\ln{(x)}}{x-1} dx = \dfrac{\pi^2}{6} \\& \\& Proof: \\& \\&

## Statistical Optimism: Investing For The Long Haul

After seeing the numerous ads for Robinhood and Acorns I thought I'd give it some thought ... so yes good marketing on their part! That's something quite rare IMO. In

## Everyone Can Be Racist: A Response to Sociological Alternatives

I want to note that I believe my argument does need some more work, and the finalized version of my argument will be available in both the Hermeneutic Pragmatism PDF

## Hermeneutic Pragmatism: The Prelude

Hey y'all! Sorry I've been less than usual in my site's upkeep. Military and college got in the way. Anyways, this post is simply to give the prelude to a

## Male Strength Standards in Specific Exercises

Many people wish to approximate their strength level through certain exercises. These exercises include the OG bench press, squat, and so on and so forth. Fitness experts over the years

## Daniel's Running Model

In the U.S. Army we run the 2mi and I've been interested in estimating times for this off others, just like how I try to estimate 100m, 200m, and 400m

## Guided Approach to Approximating π

Start with the equation: \begin{align*} &f(x) = \dfrac{1}{1+x^2}\end{align*} Integrating with respect to x from 0 to 1 yields 0.25π. What makes this a guided approach is that this integration range

## Integrals: Royal Properties

\begin{align*}& {\rm{Given}}:\int_0^\infty f(x) dx \\& \\& (1) \: \rm{Queen \: Property} \\& \\&\therefore u=(x)^{-1} \Longrightarrow\int_0^\infty f[(x)^{-1}] (x)^{-2} dx \\& \\& (2) \: \rm{Jacksonian \: Property} \\& \\&\therefore u=(x)^{-n} \Longrightarrown \int_0^\infty

## Freeletics Documentation: 115 / 372 (31%)

From the last update I did in regards to my physical fitness I do not believe I have made any progress, if not slightly regressed, and there are reasons for

## Estimating Fitness Levels: FFMI Method

I recently discovered the Fat Free Mass Index a couple of days ago. I actually have to thank the YouTube Algorithm for suggesting another video series by Vitruvian Physique on

## How Much Time is Required to Reach a Specific BF%?

I've long wondered this question so I thought I'd do some research based on past experiences and information given from various fitness outlets. I stumbled upon a good video by

## Integral of [1+(x^g)]^(-n) from 0 to ∞

\begin{align*}& \int_0^\infty \dfrac{1}{(1+x^g)^n} dx =\int_0^\infty \dfrac{(x)^{gn-2}}{(1+x^g)^n} dx \\& \\& \therefore x^g = t \: , \: x = t^{\frac{1}{g}} \Longrightarrowdx = \dfrac{t^{\frac{1}{g}-1}}{g} dt \\& \\& \therefore \int_0^\infty \dfrac{(x)^{gn-2}}{(1+x^g)^n} dx \Longrightarrow\int_0^\infty

## Integral of (1+[x^2])^(-n) from 0 to ∞

\begin{align*} & \int_0^{\infty} \dfrac{1}{(1+x^2)^n} dx \\& \\& \\& {\rm{Lemma \: (1)}}: \int_0^{\infty} \left[ f(x) \right] dx = \int_0^{\infty} \left[ \dfrac{f(\frac{1}{x})}{(x^2)} \right] dx \\& \\& {\rm{Lemma \: (2)}}: \int_0^{\frac{\pi}{2}} \left[\sin(x)\right]^{2g-1} \left[\cos(x)\right]^{2h-1}

## 200m MLR Estimate

16 April 2019 Formula (19/718 sampled) \begin{align*} \rm{200m} &\approx \rm{100m} \left[ 1.997383 + \left( \dfrac{7.633557}{\rm{60m}} \right) \right] - 11.1841 \pm 0.3 \\& \approx\rm{100m} \left[ 2 + \left( \dfrac{7.65}{\rm{60m}} \right) \right]

## Reflections: HS and College Requirements

Context I was reading through one of the various eBooks by James Gray (How to Become a Philosopher) and I wanted to see if he had written anything on Philosophy

## Why I'd Support A Negative Income Tax (NIT)

Let me start off by saying I actually have to thank someone I formerly worked with, Kelly Hernandez. We got into a discussion about UBI, the poor, etc. and from

## Using a Simple Integral to Solve a Much Harder One

\begin{align*}\displaystyle I & = \int_{\alpha}^{\beta} (e)^{x^n} \: dx =\sum \limits_{\gamma=0}^\infty \left[ \dfrac{(\beta)^{n \gamma +1}-(\alpha)^{n \gamma +1}}{(n \gamma +1) (\gamma ) !} \right]\\& \\& \therefore IBP \\&\oplus \Longrightarrow (e)^{x^n} \: ;

## I'm an INTJ - A

Sid ... INTJ's (referred to as "Architects" and "The Master Mind") are a very rare personality type. They constitute ~ 2.1% of the populace (in regards to males ~3.3%). I

## Integral of [a(x^n)+b]/[c(x)+d]

\begin{align*}I = \displaystyle \int_\alpha^\beta\dfrac{a(x)^n+b}{cx+d} \: dx &= \displaystyle \dfrac{a}{c} \int_\alpha^\beta\dfrac{(x)^n+ \frac{b}{a}}{x+\frac{d}{c}} \: dx \\&= \displaystyle \dfrac{a}{c} \int_\alpha^\beta\dfrac{(x)^n+ \Delta_1}{x+\Delta_2} \: dx \\& \therefore \: u=x+\Delta_2 \: \Longrightarrow \: u\mid_{\alpha+\Delta_2=\Delta_3}^{\beta+\Delta_2=\Delta_4} \\& \therefore

## Walking / Running Calories Burned Based on MET

Walking / Running Calories Burned Based on MET by C. D. Chester Using previous data from my article on MET Values to accurately calculate caloric burn (based on weight and

## Integral of 1/(x^n+1) from 0 to ∞

\begin{aligned} I = \int_0^\infty \dfrac{1}{(x)^n+1} dx  = \dfrac{\pi}{n\sin{( \frac{\pi}{n}} )} \end{aligned} \begin{aligned} \therefore \rho=\left[ (x)^n+1 \right]^{-1} \:;\: \rho \mid_0^1 \: \Longrightarrow d\rho=\dfrac{-n(x)^{n-1}}{\left[ (x)^n+1 \right]^2} \: dx\end{aligned} \begin{aligned} \therefore (n)^{-1} \int_0^1 \left[

## Multiplication ... But With Sigma Notation?

So most people know \begin{aligned} 2 \times 2 = 4 \end{aligned} and the basic methods taught to us in school using carries (base 10 system), but what if we introduced

## The Riemann Zeta Function Using The Pythagorean Theorem​

The Riemann Zeta Function Using The Pythagorean Theorem by C. D. Chester begin{aligned} int_0^infty dfrac{mathrm{e}^{-bx}sinleft(axright)}{a} : dx= dfrac{1}{b^2+a^2} :; a ne 0, b>0 end{aligned} This result can be easily found using

## Creator Spotlight - Zachary Lee

Zachary Lee "Obsessed with Integrals" https://philosophicalmath.wordpress.com/ Zachary's site is very straightforward, unlike the majority of my early work. My earliest work concerned primarily finding quality sites or online PDFs to

## Integral of 1/[(x^3)+1] from 0 to ∞

I=∫∞01x3+1dx=2π31.5≈1.209199576156145 Partial Fraction Decomposition Method \begin{aligned} \int_0^{\infty} \dfrac{1}{(x+1)(x^2-x+1)} \,dx \end{aligned}.\begin{aligned} \int_0^{\infty} \dfrac{1}{3(x+1)} \,dx+ \int_0^{\infty} \dfrac{x-2}{3(x^2-x+1)} \,dx \end{aligned}.\begin{aligned} \dfrac{1}{3} \int_0^{\infty} \dfrac{1}{x+1} \,dx-\dfrac{1}{3} \int_0^{\infty} \dfrac{x-2}{x^2-x+1} \,dx \end{aligned}.\begin{aligned} \left[\dfrac{1}{3} \ln{(x+1)}\right]\mid_0^{\infty}-\dfrac{1}{6}\int_0^{\infty} \dfrac{2x-1}{x^2-x+1} \,dx+\dfrac{1}{2}\int_0^{\infty} \dfrac{1}{x^2-x+1}

## 400m Estimate Using Multiple Linear Regression

Context In 2018 I saw a post: Predicting 800m Timesby Sam Harding In it he used Multiple Linear Regression to perform more and more accurate 800m estimations. I had done

## 1RM Formulae and its Applications

Context Earlier today I did a small workout using a hexagon bar (deadlift alternative). During it I managed to do 5 x 255 lb. I wondered as I got to

## Swainson et al. (WHtR) Body Fat Calculator

After perusing PubMed for awhile I have found various articles/studies on predicting body fat. You can find some here. Anyways, this one comes from one published May 11th, 2017. It

## NSCA's Macronutrient Training Guidelines

Daily Nutrient Recommendations Macronutrient g / kg / day Protein 1.2 - 2 Carbohydrate(general training) 5 - 7 Carbohydrate(athlete training) 7 - 10 Fat The rest of the calories. Minimum

## NASM's Macronutrient Plan for Adults/Athletes

Protein "The primary function of protein is to build and repair body tissues and structures. It is also involved in the synthesis of hormones, enzymes, and other regulatory peptides. Additionally,

## Radu Antoniu's Macronutrient Plans for Fat Loss and Bulking

Fat Loss Plan "So there are 3 ways to create an energy deficit: increase total physical activity, eat less or do a bit of both at the same time. The

## Fitness Plans

Below comprises 11 fitness programs/plans I offer. Once you've purchased a plan expect an intial fitness goal and evaluation via email. - C. D. Chester All Products General Nutrition /

## Estimating Caloric Burn With MET Values and EPOC

What is a MET? MET stands for Metabolic Equivalents. It is an index of energy expenditure through "the ratio of the rate of energy expended during an activity to the

## Maximal Muscular Potential for Natural Athletes Calculator

In May 2018 I published an article built off a long time personal trainer and competition athlete: Martin Berkhan. I put off making the calculator for my article on it

## Freeletics Documentation: Summary of Exercises and Workouts

These are all of the exercises and pre-made workouts on the Freeletics app. This will not include the drills or intervals as they vary based on the coach's evaluation of

## Freeletics Documentation: The Introduction

Context For many years I've always had the same selfish goal. To look like something out of a superhero movie (but more natural looking). This year I think it will

## Response to Kyle Osborne's "What I Learned From Watching Ben Shapiro for a Week"

Kyle Osborne is a writer on Medium. I am responding to his article titled What I Learned From Watching Ben Shapiro for a Week. I promised him I would more formally

## Notable Articles on Medium (UPDATED 6/6/18)

So I peruse the internet for discussions (both critiques and solutions) on various topics. Medium usually is where I find the more written-out formal arguments and YouTube (YT) is more

## Other Personal Outlets

So I also publish on Medium. You can see my articles as stories over there. Here's the link: C. D. Chester's Latest Medium Posts Everything I post on this website starting

## Thoughts on the Negative Income Tax

Introduction Recently I was in a discussion on poverty, helping the poor, subsidizing education, etc. (socialist and liberal ideas/theories) with a co-worker. I, being a very libertarian capitalist, was confronted

## A Discussion on Divine Command Theory With a Theistic Friend

Introduction Earlier today I had a conversation with a religious friend of mine (at least I strongly assume his views as being religious).  I should note that I am a

## Online Book PDF's PII (Updated 5/26/18)

Adam Smith The Wealth of Nations - An Inquiry Into the Nature and Causes of the Wealth of Nations Anarchism Anarchy, State, and Utopia by Robert Nozick Aristotle Poetics The

## VO2 Max and its Relations

References: VO2 max by Brian Mackenzie Estimation of  VO2max from the ratio between HRmax and HRrest – the Heart Rate Ratio Method by Uth et al VO2 max from a one mile

## Stride Length Estimates and Relative Calories Burned

Use these estimations to figure out how many steps it takes you to walk a kilometer if you don't already know your stride length. You then estimate how far you

## 400m Potential Calculators (UPDATED 5/23/18)

This test is designed to measure anaerobic capacity. All you have to do is run a 100m, wait 5min, and run a 400m. Enter the times in the appropriate spots

## Calories Burned While Walking or Running Calculator

I should note that the KG -KM Ratio Estimate was first made aware to me by Radu Antoniu in his video Cardio for Fat Loss. In it he states,

## Female Fitness Multi-Calculator

An adapted version of the Male Fitness Multi-Calculator with the obvious equations fitting the female standards.

## Male Fitness Multi-Calculator

I spent a good 4 hours making this calculator and transposing it onto this page. I must thank uCalc.pro for allowing this to happen.

## MATH 341 - Number Theory

What is Number Theory? by the Mathematics Department in Brown University MATH 341 is an upper division mathematics class taught at CSULB. In it's course description it defines the class

## Online Book PDFs

Note that all are links to PDFs to other websites. Some are from .edu sources and others not so much. Also, some of these PDFs take a long time to